Potassium Chloride 3:4 solution 30ml. How many milliliters of a potassium 1:20 solution and 4:5 solution do you need to prepare the order?
How do you define a 3:4 solution of KCl?
How do you figure out this problem
This is a two part question in which requires the use of the Alligation calculation method.
1) you will need to change the 3:4, 1:20, and 4:5 into their percentage parts.
How you do this is by simply dividing (remember 3:4 is the same as the fraction 3/4) so 3 divided by 4 gives you 75%.
2) Next you will need to plug in these number to the Alligation calculation table (this tic-tac-toe table). 80% top left corner, 5% in the bottom left corner. 80-5= 75 therefore, 75% goes into the middle square which is your desired does. 80-75= 5 so 5 parts goes into the bottom right corner. 75-5=70 therefore, 70parts goes into the top right corner. 70+5=75 which goes into the square between 70 and 5, to represent the total number of parts.
3) Now you just need to apply the numbers acquired into the next formula. so, the answer of mL required for the 4:5 (80%) is as follows; 70/75=0.93*30=28 mL (this is ONLY half of the answer.
1:20 (5%) 5/75=0.067*30=2 mL.
4) You will need 28 mL of the 4:5 solution and 2 mL of the 1:20 solution to prepare the order.
To solve this problem, we need to set up an equation based on the given information. Let's denote the volume of the potassium 1:20 solution as x milliliters and the volume of the potassium 4:5 solution as y milliliters.
According to the given information, we have:
Volume of potassium 1:20 solution + Volume of potassium 4:5 solution = Total volume needed
x + y = 30 ml ..........(Equation 1)
Now, let's set up an equation based on the ratio of potassium chloride in the two solutions.
For the potassium 1:20 solution, the concentration of potassium chloride is 1 part in every 20 parts of the solution. So, the ratio of potassium chloride to the potassium 1:20 solution is 1:20.
For the potassium 4:5 solution, the concentration of potassium chloride is 4 parts in every 5 parts of the solution. So, the ratio of potassium chloride to the potassium 4:5 solution is 4:5.
According to the given information, the potassium chloride concentration in the final solution is 3 parts in every 4 parts. So, the ratio of potassium chloride in the final solution is 3:4.
Let's set up another equation based on the ratio of potassium chloride:
(Potassium chloride in x ml of 1:20 solution) + (Potassium chloride in y ml of 4:5 solution) = (Potassium chloride in 30 ml of 3:4 solution)
To convert the ratios to a common denominator, we need to multiply the ratios by their respective factors:
(1/20)x + (4/5)y = (3/4)(30) ml
(1/20)x + (8/20)y = (90/4) ml
(1/20)x + (2/20)y = (90/4) ml
(1/20)x + (1/10)y = (90/4) ml ..........(Equation 2)
Now, we need to solve the system of equations (Equation 1 and Equation 2) to find the values of x and y.
Multiplying Equation 1 by -2, we get:
-2(x + y) = -2(30)
-2x - 2y = -60 ..........(Equation 3)
Now we can add Equation 3 to Equation 2:
(-2x - 2y) + (x/20 + y/10) = -60 + (90/4)
(-2x + x/20) + (-2y + y/10) = -60 + (90/4)
(-40x + x + (-20y + y))/20 = -60 + (90/4)
(-39x - 19y)/20 = -60 + (90/4)
Now, we can simplify the equation:
(-39x - 19y)/20 = (-240 + 180)/4
(-39x - 19y)/20 = (-60)/4
(-39x - 19y)/20 = -15
To remove the fraction, we can multiply both sides by 20:
-39x - 19y = -15(20)
-39x - 19y = -300 ..........(Equation 4)
Now, we can solve Equation 3 and Equation 4 simultaneously as a system of linear equations to find the values of x and y.
By solving the system of equations, we can find the values of x and y:
Equation 3: -2x - 2y = -60 => x + y = 30 (as Equation 1)
Equation 4: -39x - 19y = -300
To solve this system, we can use any method like substitution or elimination. Let's use the elimination method:
Multiply Equation 3 by 19:
19(x + y) = 19(30)
19x + 19y = 570 ..........(Equation 5)
Now, subtract Equation 5 from Equation 4:
(-39x - 19y) - (19x + 19y) = -300 - 570
-39x - 19y - 19x - 19y = -870
-58x - 38y = -870
Simplify the equation:
-58x - 38y = -870
2(29x + 19y) = 2(435)
29x + 19y = 435 ..........(Equation 6)
Now, we have a new system of equations:
Equation 6: 29x + 19y = 435
Equation 4: -39x - 19y = -300
Adding Equation 6 and Equation 4:
(29x + 19y) + (-39x - 19y) = 435 - 300
29x - 39x + 19y - 19y = 135
-10x = 135
Divide both sides by -10:
x = -13.5
Now, substitute this value of x into Equation 1 to find y:
-13.5 + y = 30
y = 30 + 13.5
y = 43.5
Therefore, you would need 13.5 milliliters of the potassium 1:20 solution and 43.5 milliliters of the potassium 4:5 solution to prepare the order.