How many grams of a stock solution that is 92.5 percent h2s04 by mass would be needed to make 250 grams of a 35% by mass solution?
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To solve this problem, we can use the concept of mass percent, which is the ratio of the mass of solute to the mass of the solution (solute + solvent), expressed as a percentage.
Let's break down the problem into steps:
Step 1: Define the unknown.
Let's call the mass of the stock solution we need to find x grams.
Step 2: Set up the equation.
The mass percent equation is:
(grams of solute / grams of solution) × 100% = mass percent
For the stock solution:
92.5% = (grams of solute / x) × 100%
For the final solution:
35% = (grams of solute / 250) × 100%
Step 3: Solve for the unknown.
Rearrange the equations to solve for grams of solute in each case:
92.5% = (grams of solute / x) × 100% → grams of solute = (92.5% / 100%) × x
35% = (grams of solute / 250) × 100% → grams of solute = (35% / 100%) × 250
Step 4: Set the expressions equal to each other and solve for x.
(92.5% / 100%) × x = (35% / 100%) × 250
First, simplify the equation:
0.925x = 0.35 × 250
Now, solve for x:
0.925x = 87.5
Divide both sides by 0.925:
x = 87.5 / 0.925
Calculating the value, we get:
x ≈ 94.59 grams
Therefore, approximately 94.59 grams of the stock solution that is 92.5% H2SO4 by mass would be needed to make 250 grams of a 35% by mass solution.