How many grams of a stock solution that is 92.5 percent H2SO4 by mass would be needed to make 250 grams of a 35.0 percent by mass solution?
Can you please teach me how to do this? I get the other stoichiometry stuff, but this one tripped me up because I don't know how to set up the problem.
You want 250 g of 35% H2SO4 by mass. That is 35 g/100 g. How much is that in 250 g? That will be 35g x (250g/100g) = 87.5 grams. (You can check that by 87.5/250 = 0.35 so that must be right.).
Now, you know you want 87.5 g, how much of the 92.5% stuff do you nee to obtain that.
100 g soln x (87.5g/92.5g) = about 94g. You would then want to add 250-94 = about 156 g water to make a total of 250 g. You need to do this more accurately. You can check out the final solution by 94.5g soln x (92.5/100) = approximately 87.5 g. Again, you should do this more accurately.
To solve this problem, you will need to apply the concept of mass percent and the method of mixing solutions. Here's a step-by-step guide to help you solve it:
Step 1: Understand the question
In this problem, you are asked to determine the amount of the stock solution (92.5% H2SO4) required to prepare a 35.0% H2SO4 solution.
Step 2: Define the variables
Let's define the following variables:
- mass_stock = mass of the stock solution (in grams)
- concentration_stock = concentration of the stock solution (92.5%)
- mass_solution = mass of the final 35.0% solution (250 grams)
- concentration_solution = concentration of the final 35.0% solution
Step 3: Set up the equation
To solve the problem, we need to find the mass of the stock solution required. We can set up the following equation using the mass percent formula:
(mass_stock x concentration_stock) + (mass_solution x concentration_solution) = mass_solution x concentration_solution
Step 4: Calculate the mass of the stock solution
In the given problem, the stock solution is 92.5% H2SO4. This means that for every 100 grams of the stock solution, 92.5 grams is H2SO4. Therefore, the mass of H2SO4 in the stock solution can be calculated as:
mass_H2SO4_stock = (concentration_stock / 100) x mass_stock
Step 5: Solve for the unknown variable (mass_stock)
Now, substitute the values into the equation and solve for the unknown variable (mass_stock). Rearrange the equation to isolate mass_stock:
mass_stock = (mass_solution x concentration_solution - mass_H2SO4_stock) / (concentration_stock - concentration_solution)
Step 6: Calculate the mass_stock
Plug in the known values into the equation and calculate the mass_stock:
mass_stock = (250 grams x 0.35 - mass_H2SO4_stock) / (0.925 - 0.35)
Step 7: Calculate the mass_H2SO4_stock
Using mass_H2SO4_stock = (concentration_stock / 100) x mass_stock, calculate the mass of H2SO4 in the stock solution.
Step 8: Substitute the value of mass_H2SO4_stock and calculate the mass_stock
Now, substitute the value of mass_H2SO4_stock into the equation calculated in step 6:
mass_stock = (250 grams x 0.35 - mass_H2SO4_stock) / (0.925 - 0.35)
Finally, solve this equation to find the mass_stock, which will give you the grams of the stock solution needed to make the 250-gram 35.0% solution.