How many grams of a stock solution that is 85.5 percent H2SO4 by mass would be needed to make 150 grams of a 45.0 percent by mass solution? Show all of
the work needed to solve this problem.
85.5% H2SO4 w/w means 85 g H2SO4 + 15 g H2O or 85.5 g H2SO4/100 g solution. How many grams H2SO4 will be in 150 g of that solution?
g H2SO4 = 85.5 x (150/100) = approx 128 but that's an estimate (but close).
How many g H2SO4 will be 150 g of 45% solution. That will be
45 x 150/100 = about 67 (again close) but an estimate.
So you want (128/150) * ? g = 68
? = about 68*150/128 = about 80 g. You would need to add about 70 g H2O to make 150 g total solution. I came out with 78.9 g of the 85.5% H2SO4 original solution.
Thanks!!!
To solve this problem, we need to use the concept of mass percent and then apply it to find the amount of the stock solution needed. Here's how you can solve it step by step:
Step 1: Understand the problem
We need to find out how many grams of a stock solution, which is 85.5% H2SO4, is required to make 150 grams of a 45.0% H2SO4 solution.
Step 2: Determine the amount of H2SO4 in the final solution
Since we know that the final solution should be 45.0% H2SO4, we can calculate the mass of H2SO4 in the final solution as follows:
Mass of H2SO4 in the final solution = Mass of the final solution × Percentage of H2SO4
= 150 grams × 0.45
= 67.5 grams
Step 3: Determine the amount of H2SO4 in the stock solution
Since we have the percentage of H2SO4 in the stock solution (85.5%), we can calculate the mass of H2SO4 in the stock solution as follows:
Mass of H2SO4 in the stock solution = Mass of the stock solution × Percentage of H2SO4
= x grams × 0.855
= 0.855x grams
Step 4: Set up the equation
We know that the mass of H2SO4 in the final solution is equal to the mass of H2SO4 in the stock solution. Therefore, we can set up the equation:
0.855x grams = 67.5 grams
Step 5: Solve for x
To solve for x, divide both sides of the equation by 0.855:
x = 67.5 grams / 0.855
x ≈ 78.95 grams
Therefore, approximately 78.95 grams of the stock solution that is 85.5% H2SO4 by mass would be needed to make 150 grams of a 45.0% H2SO4 solution.
Note: In this explanation, we assumed that the mass of the solution does not change during the mixing process.