A science teacher has a supply of 5% hydrochloric acid and a supply of 65% hydrochloric acid (HCl). How much of each solution should the teacher mix together to get 42 mL of 45% HCl for an experiment?
a. The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
b. The teacher will need 28 mL of the 5% solution and 14 mL of the 65% solution.
c. The teacher will need 14 mL of the 5% solution and 14 mL of the 65% solution.
d. The teacher will need 28 mL of the 5% solution and 28 mL of the 65% solution.
A. I googled it
5x + 65(42-x) = 45*42
thnx
Well, it seems like the science teacher is going to have a mixing party! To make a 45% HCl solution, they will need a combination of the 5% and 65% solutions. Let's make some magic happen in the lab with some calculations.
Let's assume they need "x" mL of the 5% solution and "y" mL of the 65% solution.
To find out how much HCl is in the solution, we can use the equation:
0.05x + 0.65y = 0.45 * 42
Now, let's simplify and solve this equation to unlock the secret combination of solution quantities.
0.05x + 0.65y = 18.9
Okay, let me put on my mathematician hat. Crunching some numbers...tick tock, tick tock.
After some calculations, I've got the answer for you. Drumroll, please!
The answer is option **: The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
Now the teacher is all set for their experiment. Just don't let them mix up their test tubes with their dance moves!
To find the answer to this question, we need to calculate the amount of each solution that should be mixed to get a 42 mL solution of 45% HCl.
Let's start by assigning variables to represent the amount of each solution we need. Let's call the amount of the 5% solution "x" (in mL) and the amount of the 65% solution "y" (in mL).
The total volume of the solution we want is 42 mL, so we have the equation: x + y = 42
Now, let's consider the amount of HCl in each solution. The 5% solution contains 5% of HCl, which means x mL of the 5% HCl solution contains 0.05x mL of HCl. Similarly, the 65% solution contains 65% of HCl, which means y mL of the 65% HCl solution contains 0.65y mL of HCl.
The total amount of HCl in the final solution is 45% of 42 mL, which is 0.45 * 42 = 18.9 mL.
So, our second equation is: 0.05x + 0.65y = 18.9
Now, we have a system of linear equations:
x + y = 42
0.05x + 0.65y = 18.9
To solve this system of equations, we can use substitution or elimination method.
Using the elimination method, we can multiply the first equation by -0.05 and then add it to the second equation:
-0.05(x + y) = -0.05(42)
-0.05x - 0.05y = -2.1
0.05x + 0.65y = 18.9
By adding the two equations, we eliminate the x term:
(0.05x - 0.05x) + (0.65y + 0.05y) = 18.9 - 2.1
0.7y = 17.8
Dividing both sides of the equation by 0.7 gives us:
y = 17.8 / 0.7 = 25.43 mL
Now, we can substitute the value of y back into the first equation to find x:
x + 25.43 = 42
x = 42 - 25.43 = 16.57 mL
Therefore, the teacher will need approximately 16.57 mL of the 5% solution and 25.43 mL of the 65% solution.
Comparing this with the answer choices, we can see that option d. The teacher will need 28 mL of the 5% solution and 28 mL of the 65% solution is not correct.
The correct answer is:
c. The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.