What mass of a concentrated solution of nitric acid (68.0% HNO3 by mass) is needed to prepare 400.0 g of a 10.0% solution of HNO3 by mass?

To solve this problem, we need to find out how much HNO3 is in the 10.0% solution first.

1. Calculate the mass of HNO3 in the 10.0% solution: Mass of HNO3 = 10.0% of 400.0 g = 0.10 * 400.0 g = 40.0 g

2. Determine the mass of HNO3 in the concentrated solution: Since the concentrated solution is 68.0% HNO3 by mass, the mass of HNO3 in the solution is 68.0% of the total mass of the solution. Let's denote the total mass of the solution as x. So, we have: 0.68 * x = 40.0 g

3. Solve the equation for x: x = 40.0 g / 0.68 = 58.82 g

So, you would need 58.82 g of the concentrated solution to prepare 400.0 g of a 10.0% solution of HNO3 by mass.