Consider the following linear program.
Min 5A + 5B
s.t. 1A + 3B ≤ 15
3A + 1B ≥ 14
1A − 1B = 2
A, B ≥ 0
(a) Show the feasible region.
(b) What are the extreme points of the feasible region?
smaller A-value (A, B) = ( ? )
larger A-value (A, B) = ( ? )
(c) Find the optimal solution using the graphical solution procedure.
(A, B) = ( ? )
Answers
The optimal solution is (A, B) = (2, 4), where the minimum value of the objective function 5A + 5B is achieved.
The feasible region can be determined by graphing the given constraints on a coordinate plane.
The constraint 1A + 3B ≤ 15 can be rewritten as B ≤ (15 - A)/3, which represents a line with a slope of -1/3 passing through the point (15, 0). The constraint 3A + 1B ≥ 14 can be rewritten as B ≥ 14 - 3A, representing a line with a slope of -3 passing through the point (0, 14). The constraint 1A - 1B = 2 represents a line with a slope of 1 passing through the points (-2, -4) and (0, 2). The feasible region is the intersection of the shaded regions defined by these three constraints and the non-negative region of the coordinate plane.
(b) The extreme points of the feasible region can be found at the vertices where the boundaries of the shaded regions intersect. By analyzing the graph, we can identify the extreme points as follows:
Smaller A-value: (2, 4)
Larger A-value: (4, 2)
(c) To find the optimal solution using the graphical solution procedure, we need to evaluate the objective function 5A + 5B at each of the extreme points. By substituting the values of A and B from the extreme points, we can calculate:
For (2, 4): 5(2) + 5(4) = 10 + 20 = 30
For (4, 2): 5(4) + 5(2) = 20 + 10 = 30
Both extreme points yield the same objective function value of 30. Therefore, the optimal solution is (A, B) = (2, 4), where the minimum value of the objective function 5A + 5B is achieved.
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Related Questions
suppose that japan is considering placing trade restrictions on imports of u.s. pharmaceuticals. it could choose either a tariff or a quota, which would be designed to reduce imports by the same quantity. which of these groups would be indifferent between the tariff and the quota?a. jpanese producers of pharmaceuticals b. Japanese government c. Japanese buyers of pharmaceuticals d. U.S. producers of pharmaceuticals
Answers
The group that would be indifferent between the tariff and the quota would be Japanese buyers of pharmaceuticals.
Both the tariff and the quota would result in a reduction of imports of U.S. pharmaceuticals, which would likely lead to an increase in the price of these products in Japan.
Japanese producers of pharmaceuticals would benefit from a reduction in competition, and the Japanese government may prefer one policy over the other based on factors such as revenue collection or political considerations. U.S. producers of pharmaceuticals would likely be negatively impacted by either policy.
However, Japanese buyers of pharmaceuticals would be indifferent between the two policies since both would result in a reduction of imports and an increase in price, which would be passed on to them.
Therefore, they would not have a preference for one policy over the other.
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Apples are $1.79 per lb at Food Lion. If I purchase 3.8 lbs, how much sure I expect to pay?
Answers
Answer:
$6.80
Step-by-step explanation:
1.79 x 3.8 = 6.802
So $6.80
Which expression is equivalent to ¼ m + ¾ m - ⅜ (m+1)?
⅝ m + ⅜
⅝ m - ⅜
⅜ m + ⅝
⅜ m - ⅝
Answers
Answer:
5/8m+3/8
Step-by-step explanation:
1/4m+3/4m-3/8(m+1)
1/4m+3/4m-3/8m+3/8
5/8m+3/8
Answer:
5/8m + 3/8
Step-by-step explanation:
1/4m + 3/4m - 3/8 (m + 1)
1/4m + 3/4m - 3/8m + 3/8
5/8m + 3/8
Triangle SAM is congruent to Triangle REN. Find x and y.
Answers
\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)
the area of a rectangle is what
Answers
Answer:
The area of rectangle is Length × Breadth
Step-by-step explanation:
You have already learnt that perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed figure while area is the part of plane or reason occupied by the closed figure.
\( \sf \: Squares \: and \: Rectangles\)
Ananya and samira made pictures. Ananya made her picture on a rectangular sheet of length 60 cm and breadth 20 cm while samira made hers on a rectangular seat of length 40 cm and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for farming is the cost of farming is $3.00 per cm?
If the cost of lamination is $2.00 per cm², who has to pay more for lamination?
For finding the cost of farming, we need to find perimeter and then multiply it by the rate for farming. For finding the cost of lamination we need to find area and then multiply it by the rate of lamination.
Example:-Find the area of the rectangle whose Length is 4 cm and breadth/width is 6 cm .
Answer:
The area of the rectangle is 24 cm²
Step-by-step explanation:
Length of rectangle = 4 cm
Breadth of rectangle = 6 cm
\( \bf \: Formula \: used\)
\( \sf \: Area_ { \{Rectangle \}} = Length × Breadth\)
Now put values
\( \sf \: Length = 4 cm \)
\( \sf \: Breadth = 6 cm\)
\( \sf \: Length × Breadth = 4 × 6 \: cm \)
\( \sf \implies 24 \: cm \ {}^{2} \)
Always remember if we find area :-
After units like centimetres,metres we always put (²) on these units.
Like :- 26 cm², 56 m ²
In words = Twenty six centimetre square, Fifty six centimetre square
Required Answer :The area of rectangle is 24 cm²
Additional informatioNPerimeter
Parallelogram = 2(Base + Height)Triangle = a + b + cRectangle = 2(Length + Width)Square = 4×sideTrapezoid = Base + Base + side + sideRhombus = 4 × sideHexagon = 6 × sideArea
Square area formula: = side×sideRectangle area formula: = L × BCircle area formula: = πr²Circle sector area formula: = r² × angle / 2.Ellipse area formula: = Axis× Axis × πTrapezoid area formula: = (base + base) × h / 2.Area of a Triangle = A = ½ (b × h)♦ Area of Rectangle
Length × Breadth\( \underline{ \rule{140pt}{4pt}}\)
Additional Information :-Area - Region occupied by figure is called area.
\( \large \bf{ \mathfrak{{More \: Formulas \: \red{( Area)}}}}\)
\( \large \sf \leadsto \: triangle = \frac{1}{2} \times bh\)
\(\large \sf \leadsto \: \: Rectangle \: = \: lb\)
\(\large \sf \leadsto \: \: Square \: = {s}^{2} \)
\(\large \sf \leadsto \: \: Parallelogram \: = \: bh\)
\(\large \sf \leadsto \: \: Rhombus \: = \: \frac{1}{2} \times \: d1 \times d2\)
\(\large \sf \leadsto \: \: Trapezium \: = \frac{1}{2} \times (x + y) \times h\)
\(\large \sf \leadsto \: \: Quadrilateral \: = \: \frac{1}{2} \times d(h1 + h2)\)
\(\large \sf \leadsto \: Circle \: = {\pi \: r}^{2} \)
\(\large \sf \leadsto \: \: Equilateral \triangle \: = \frac{ \sqrt{3} }{4} \times {s}^{2} \)
Hello This is question of Account of class 11 from chapter Accounting equation if you can solve this question then please hive me it's answer it's my homework for presenting tomorrow
Question No. HW 2 Ans.:Assets Rs.3,10,000; Capital Rs. 2,50,000; Liabilities Rs.60,000 A Company provides you the following business transactions : (a) Business commenced with cash Rs.70,000 and bank balance Rs.1,30,000 and goods Rs.50,000 (b) Goods purchased of Rs.80,000 in cash. (c) Goods purchased from Johny traders of Rs.60,000 on credit. (d) Goods sold of Rs.40,000 in cash. (e)Goods sold to Tony traders for Rs.30,000 on credit. Required : Accounting Equation
Answers
The new accounting equation after considering the transaction are:
a. Assets = Rs.3,60,000, Capital = Rs.2,50,000, Liabilities = Rs.60,000b. Assets = Rs.3,50,000, Capital = Rs.2,50,000, Liabilities = Rs.60,000c. Assets = Rs.3,50,000, Capital = Rs.2,50,000, Liabilities = Rs.1,20,000d. Assets = Rs.3,90,000, Capital = Rs.2,90,000, Liabilities = Rs.1,20,000e. Assets = Rs.3,90,000, Capital = Rs.2,90,000, Liabilities = Rs.1,20,000What is an Accounting Equation?This refers to the formula that shows sum of a company's liabilities and shareholders' equity are equal to its total assets (Assets = Liabilities + Equity).
Data
Assets = Rs.3,10,000
Capital = Rs.2,50,000
Liabilities = Rs.60,000
Now, let's analyze each transaction and update the accounting equation accordingly:
(a) Business commenced with cash Rs.70,000 and bank balance Rs.1,30,000 and goods Rs.50,000Cash increases by Rs.70,000
Bank balance increases by Rs.1,30,000
Goods increase by Rs.50,000
Therefore, the new accounting equation becomes:
Assets = Rs.3,60,000 (Rs.3,10,000 + Rs.70,000 + Rs.1,30,000 + Rs.50,000)
Capital = Rs.2,50,000
Liabilities = Rs.60,000
(b) Goods purchased of Rs.80,000 in cashCash decreases by Rs.80,000
Goods increase by Rs.80,000
Therefore, the new accounting equation becomes:
Assets = Rs.3,50,000 (Rs.3,60,000 - Rs.80,000 + Rs.80,000)
Capital = Rs.2,50,000
Liabilities = Rs.60,000
(c) Goods purchased from Johnny traders of Rs.60,000 on creditLiabilities increase by Rs.60,000
Goods increase by Rs.60,000
Therefore, the new accounting equation becomes:
Assets = Rs.3,50,000
Capital = Rs.2,50,000
Liabilities = Rs.1,20,000 (Rs.60,000 + Rs.60,000)
(d) Goods sold of Rs.40,000 in cashCash increases by Rs.40,000
Capital increases by Rs.40,000
Therefore, the new accounting equation becomes:
Assets = Rs.3,90,000 (Rs.3,50,000 + Rs.40,000)
Capital = Rs.2,90,000 (Rs.2,50,000 + Rs.40,000)
Liabilities = Rs.1,20,000
(e) Goods sold to Tony traders for Rs.30,000 on creditAccounts receivable increase by Rs.30,000
Capital increases by Rs.30,000
Therefore, the final accounting equation becomes:
Assets = Rs.3,90,000
Capital = Rs.3,20,000 (Rs.2,90,000 + Rs.30,000)
Liabilities = Rs.1,20,000
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Amir solved the following equation. describe the first mistake he made.
2x-2=14
-2 -2
2x =12
2. 2
X=6
Answers
Answer:
he faked too much
Step-by-step explanation:
This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Click and drag the steps on the left to their corresponding step number on the right to prove the given statement. (A ∩ B) ⊆ Aa. If x is in A B, x is in A and x is in B by definition of intersection. b. Thus x is in A. c. If x is in A then x is in AnB. x is in A and x is in B by definition of intersection.
Answers
In order to prove the statement (A ∩ B) ⊆ A, we need to show that every element in the intersection of A and B is also an element of A. Let's go through the steps:
a. If x is in (A ∩ B), x is in A and x is in B by the definition of intersection. The intersection of two sets A and B consists of elements that are present in both sets.
b. Since x is in A and x is in B, we can conclude that x is indeed in A. This step demonstrates that the element x, which is part of the intersection (A ∩ B), belongs to the set A.
c. As x is in A, it satisfies the condition for being part of the intersection (A ∩ B), i.e., x is in A and x is in B by the definition of intersection.
Based on these steps, we can conclude that for any element x in the intersection (A ∩ B), x must also be in set A. This means (A ∩ B) ⊆ A, proving the given statement.
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There are 4 more boys than girls in a
class. If there are 16 students in the
class, how many are boys? How many are
girls?
Set up an equation to show this, and then
solve.
Answers
Answer:
There are 10 boys and 6 girls in the class
Step-by-step explanation:
The given parameters are;
The number of boys = The number of girls + 4
The number of students in the class = 16
Let x represent the number of girls in the class and let y represent the number of boys in the class
Therefore;
y = x + 4...(1)
x + y = 16...(2)
Making y the subject of equation (2) gives;
y = 16 - x
Equating the values of y from equation (1) and equation (2) gives;
x + 4 = 16 - x
Which gives;
2·x = 16 - 4 = 12
x = 12/2 = 6
x = 6
The number of girls = x = 6
From equation (1), we have;
y = x + 4 = 6 + 4 = 10
y = 10
The number of boys = y = 10.
What is the purpose of using prefixes in the metric system?
Answers
Answer: to scale the base units so that they can represent anything from a very large numeric value
Step-by-step explanation:
to scale the base units so that they can represent anything from a very large numeric value
what is the range of possible sizes for x?
Answers
Answer:
0.5 < x < 15.5
Step-by-step explanation:
Triangle Inequality Theorem
Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:
x + y > z
x + z > y
y + z > x
Combining the above inequalities, and provided y>z, the third size must satisfy:
y - z < x < y + z
The two side lengths given in the triangle of the figure are y=8.5, z=8.0, thus the possible values of x lie in the interval
8.5 - 8.0 < x < 8.5 + 8.0
0.5 < x < 15.5
A company has improved its production process. Under the old process, 11 workers could produce 4,873 units per hours and the materials cost $56 per unit of output. Workers are paid $17 per hour and the finished product is sold for $102 per unit. After the improvement, materials costs have been reduced by $14 per unit of output and it now takes 3 fewer workers to make the same amount of output. What is the percentage change in multifactor productivity? (do not use a \% sign, e.g. enter 50% as .5)
Answers
The percentage change in multifactor productivity is approximately 36.15%.
To calculate the percentage change in multifactor productivity, we need to compare the productivity before and after the improvement in the production process. The multifactor productivity is calculated by dividing the output value by the input value.
Given data for the old process:
Number of workers: 11
Output per hour: 4,873 units
Materials cost per unit: $56
Worker wage per hour: $17
Selling price per unit: $102
Given data for the improved process:
Materials cost reduction per unit: $14
Workers reduced: 3
Let's calculate the multifactor productivity before and after the improvement:
Before the improvement:
Output value = Output per hour * Selling price per unit = 4,873 * $102 = $497,046
Input value = (Number of workers * Worker wage per hour) + (Materials cost per unit * Output per hour) = (11 * $17) + ($56 * 4,873) = $5,661 + $272,488 = $278,149
Multifactor productivity before = Output value / Input value = $497,046 / $278,149 ≈ 1.785
After the improvement:
Output value remains the same = $497,046
Input value = [(Number of workers - Workers reduced) * Worker wage per hour] + [(Materials cost per unit - Materials cost reduction per unit) * Output per hour]
= [(11 - 3) * $17] + ($42 * 4,873) = $119 + $204,666 = $204,785
Multifactor productivity after = Output value / Input value = $497,046 / $204,785 ≈ 2.43
Now, let's calculate the percentage change in multifactor productivity:
Percentage change = ((Multifactor productivity after - Multifactor productivity before) / Multifactor productivity before) * 100
= ((2.43 - 1.785) / 1.785) * 100
= (0.645 / 1.785) * 100
≈ 36.15
Therefore, Multifactor productivity has changed by about 36.15 percent.
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please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111
Answers
Answer:
\(N(-1,4)\)
Step-by-step explanation:
Choose the equation that correctly shows the Commutative Property of Multiplication.
10 x3/10 = 10 x 3/10
10 +3/10 = 3/10x 10
10 x 3/10 = 3/10 x 10
10 x3/10 = 3/10 ÷ 10 IL GIVE BRAINLIEST!!!
Answers
He equation that rightly shows the Commutative Property of addition is
10 x3/10 = 3/10 x 10
The Commutative Property of Multiplication states that changing the order of the factors doesn't change the product. In other words, when you multiply two figures, it doesn't count which number comes first. The equation 10 x3/10 = 3/10 x 10 is an illustration of this property, as both sides of the equation represent the same value, indeed though the order of the factors is different.
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Which graph is best to show categorical data?
line graph
box-and-whisker plot
scatter plot
circle graph
Answers
Answer:
Bar graphs, pie charts or circle graphs
Step-by-step explanation:
Answer:
line graph
Step-by-step explanation:
thay show Categorical data mostly because it the better one
Mensa is an organization that allows people to join only if their Stanford-Binet IQs are in the top 2% of the population. Assume the population mean of Stanford-BinetIQs is 100, and the standard deviation is 15, and that the population is normally distributed. What is the probability that two randomly selected people both have Stanford-Binet IQs which qualify them for Mensa?
Answers
The probability that two randomly selected people both have Stanford-Binet IQs which qualify them for Mensa is approximately 0.000408, or 0.0408%.
To determine the probability that two randomly selected people both have Stanford-Binet IQs qualifying them for Mensa, we need to calculate the probability of an individual having an IQ in the top 2% and then multiply that probability by itself since we are interested in both individuals having qualifying IQs.
Since the population is assumed to be normally distributed with a mean of 100 and a standard deviation of 15, we can use the Z-score formula to find the probability.
First, we need to find the Z-score corresponding to the top 2% of the distribution. We can use a standard normal distribution table or a calculator to determine that the Z-score for the top 2% is approximately 2.05.
Next, we convert the Z-score into a probability using the standard normal distribution table or calculator. The probability of an individual having an IQ in the top 2% is given by the area under the curve to the right of the Z-score of 2.05.
P(Z > 2.05) ≈ 0.0202
Now, to find the probability that both individuals have qualifying IQs, we multiply the probabilities together.
P(both individuals qualify) = P(individual 1 qualifies) * P(individual 2 qualifies)
= 0.0202 * 0.0202
≈ 0.000408
Therefore, the probability that two randomly selected people both have Stanford-Binet IQs which qualify them for Mensa is approximately 0.000408, or 0.0408%.
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Help me plz!!!!!!!!!!!
Answers
Answer:
40 in^3
Step-by-step explanation:
5 x 4 x 2 = 20 x 2 = 40
in testing a hypothesis from a random sample involving three or more means, the appropriate test would be a one-way anova. True or false?
Answers
When testing a hypothesis involving three or more means, the appropriate test is a one-way ANOVA (Analysis of Variance). ANOVA is a statistical method that compares the means of two or more groups to determine if there is a significant difference between them. In the case of a one-way ANOVA, we are comparing the means of one variable across multiple groups or categories.
The one-way ANOVA test allows us to determine if the differences between the means of the groups are significant enough to reject the null hypothesis, which states that there is no significant difference between the means. If the p-value obtained from the ANOVA test is less than the chosen level of significance, we reject the null hypothesis and conclude that there is a significant difference between at least two of the means.
The area of the trapezoid is 27 square centimeters.
b1 is 13 and b2 is 5
What is the trapezoid's height, h?
Answers
Answer:
As Per Given Information
Area of Trapezoid is 27cm²
base ,b1 = 13
base , b2 = 5
we have to find the height of trapezoid .
Let the height of trapezoid be h cm .
Area of Trapezoid = ½ ( b1 + b2) × h
On Putting the value we obtain
↝ 27 = ½ ( 13+5) × h
↝ 27 × 2 = 18 × h
↝ 54 = 18 × h
↝ 54/18 = h
↝ 3cm = h
So , the height of trapezoid is 3 cm.
1. Choose the correct label for each feature of the diagram from this list.
Write its letter in the correct place in the diagram. (Not all the letters are needed.)
A The line y = 0
B
The line x = 0
с
The line x = 6
shift
D The line y=6
E The origin
10.94492
F
The line y=zx
G The line x + y = 9
H The line y=x+6
I
The line y=x-6
J
The solution of the simultaneous equations x + y = 9 and y= *
K The solution of the simultaneous equations x + y = 9 and y= 2x
2. Which point is on the line y = 6 and on the line x = 6?
3. Write the equation of any straight line that goes through the point (3,6).
Answers
Answer:
Step-by-step explanation:
Adrian took out a simple interest loan for $2000. The rate on this loan is 7% and he will pay it back in 5 years. How much money will Adrian owe at the end of 5 years including interest?
Answers
Answer:
i think its 700
Step-by-step explanation:
7%of 2000 is 140 and 140 x 5 is 700
Answer: $700 interest
Note that the formula for simple interest is I=Prt
1. Identify the Principal amount (P), rate (r), and time (t)
Principal amount=$2,000
Rate: 7% (0.07)
Time: 5 years
2. Plug the numbers into the formula; always make sure that the rate is in decimal form and the time is in years.
2,000*0.07*5=700
3. Final answer: $700
The taxi costs 2.25 for the first mile plus 15 cents for each additional tenth of a mile. For a 5.2- mile trip eric paid 10 and told the driver to keep the change as a trip how much was the drivers tip
Answers
Answer:
$1.45
Step-by-step explanation:
The computation of the driver tip is shown below:
= 2.25 + 1.5 + 1.5 + 1.5 + 1.5 + 0.3
= $8.55
And, the amount given to driver is 10
So, the driver tip is
= $10 - $8.55
= $1.45
Adding and subtracting
(6x²)-(2x)
Answers
Answer:
\(\huge \boxed{{2x(3x-1)}}\)
Step-by-step explanation:
\((6x^2)-(2x)\)
Apply rule : \(-(a)=-a\)
\(6x^2-2x\)
The expression cannot be simplified further.
Factor out 2x from the expression.
\(2x(3x-1)\)
Answer:
\((6x {}^{2}) - (2x)\)
Remove unecessary parentheses\(6x {}^{2} { - 2x}\)
Solution
\(6x {}^{2} - 2x \)
3 candies cost 90 cents. What is the cost of a candy? Let x be the cost of a candy.
Answers
x=.30
2₁/₂ ÷1₇/₈
If you dont understand the question I mean 2 whole number 1 out of 2 divided by 1 whole number 7 out of 8
Answers
The solution of the mixed fraction will be 4 / 3.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression of the mixed fraction is 2¹/₂÷1⁷/₈. The expression will be solved as,
E = 2¹/₂÷1⁷/₈
E = ( 5 / 2 ) ÷ ( 15 / 8 )
E = ( 5 / 2 ) x ( 8 / 15 )
E = 4 / 3
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10. MP Find the Error The rate of growth for a
is
home.
plant is 0.2 centimeter per 0.5 day. A
are feet.
student found the number of days for
need to
the plant to grow 3.6 centimeters to be
70w
1.44 days. Find the error and correct it.
+1
Answers
Answer:
the error is how many days it will take for the plant to grow 3.6 centimeters they have 1.44 but the correct answer is 9 days.
Step-by-step explanation:
it will take the plant 9 days to grow 3.6 centimeters
Divide 144g in the ratio 7: 11
Answers
Answer:
88:56 = 11:7
Step-by-step explanation:
Step One
Add the two ratios together 11 + 7 = 18
Now set up a ratio to solve for 11 parts out of 18
11:18 = x:144 Proportion
11 / 18 = x / 144 Equation: Cross mulitiply
11*144 = 18x Combine the left side
1584 = 18x Divide by 18
1584 / 18 = x
88 = x
That is the larger amount (11 is larger than 7)
Find the smaller amount
144 - 88 = 56
The two amounts are in the ratio of 11:7
88:56 = 11:7
I hopes this helps a little bit
Answer:
56g and 88g
Step-by-step explanation:
7x+11x=144
18x=144
x=144/18
x=8
7x=7*8=56g
11x=11*8=88g
write an equation to represent the pattern
m. n.
2. 4
3. 6
4. 8
Answers
Answer:
\(\frac{n}{m} =2\)
hope this helps! :)
Answer:
N÷M=2
Step-by-step explanation:
If you divide these they equal out to 2
How many grams of mercury metal will be deposited from a solution that contains Hg^2+ ions if a current of 0.935 A is applied for 55.0 minutes.
Answers
approximately 9.25 grams of mercury metal will be deposited from the solution containing Hg²+ ions when a current of 0.935 A is applied for 55.0 minutes.
To determine the mass of mercury metal deposited, we can use Faraday's law of electrolysis, which relates the amount of substance deposited to the electric charge passed through the solution.
The equation for Faraday's law is:
Moles of Substance = (Charge / Faraday's constant) * (1 / n)
Where:
- Moles of Substance is the amount of substance deposited or produced
- Charge is the electric charge passed through the solution in coulombs (C)
- Faraday's constant is the charge of 1 mole of electrons, which is 96,485 C/mol
- n is the number of electrons transferred in the balanced equation for the electrochemical reaction
In this case, we are depositing mercury (Hg), and the balanced equation for the deposition of Hg²+ ions involves the transfer of 2 electrons:
Hg²+ + 2e- -> Hg
Given:
- Current = 0.935 A
- Time = 55.0 minutes
First, we need to convert the time from minutes to seconds:
\(Time = 55.0 minutes * 60 seconds/minute = 3300 seconds\)
Next, we can calculate the charge passed through the solution using the equation:
\(Charge (Coulombs) = Current * Time\\Charge = 0.935 A * 3300 s\)
Now, we can calculate the moles of mercury deposited using Faraday's law:
Moles of mercury = (Charge / Faraday's constant) * (1 / n)
Moles of mercury = (0.935 A * 3300 s) / (96,485 C/mol * 2)
Finally, we can calculate the mass of mercury using the molar mass of mercury (Hg):
Molar mass of mercury (Hg) = \(200.59 g/mol\)
Mass of mercury = Moles of mercury * Molar mass of mercury
Mass of mercury = [(0.935 A * 3300 s) / (96,485 C/mol * 2)] * 200.59 g/mol
Calculating this, we find:
Mass of mercury ≈ \(9.25 grams\)
Therefore, approximately 9.25 grams of mercury metal will be deposited from the solution containing Hg²+ ions when a current of 0.935 A is applied for 55.0 minutes.
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