Concentrated HNO3 is 68% by mass.Density of the solution is 1.25g/cm^3.Calculate the volume of the solution containing 20 gms of HNO3.

To find the volume of a concentrated nitric acid (HNO3) solution that contains 20 grams of HNO3, we can follow a systematic approach. We know the solution is 68% HNO3 by mass and has a density of 1.25 g/cm³. Let's break down the calculation step by step.

Step 1: Determine the mass of the solution

Since the solution is 68% HNO3 by mass, this means that in every 100 grams of the solution, there are 68 grams of HNO3. We can set up a proportion to find out how much solution is needed to obtain 20 grams of HNO3.

• Let \( x \) be the mass of the solution required.
• Using the percentage, we can express this as:

68 grams HNO3 / 100 grams solution = 20 grams HNO3 / x grams solution

Now, we can cross-multiply to solve for \( x \):

68x = 2000

Dividing both sides by 68 gives:

x = 2000 / 68 ≈ 29.41 grams

Step 2: Calculate the volume of the solution

Now that we know the mass of the solution required is approximately 29.41 grams, we can find the volume using the density of the solution. The formula for density is:

Density = Mass / Volume

Rearranging this formula to find volume gives us:

Volume = Mass / Density

Substituting in our values:

Volume = 29.41 grams / 1.25 g/cm³

Calculating this gives:

Volume ≈ 23.53 cm³

Final Result

Therefore, the volume of the concentrated HNO3 solution that contains 20 grams of HNO3 is approximately 23.53 cm³. This calculation illustrates how we can use the properties of solutions, such as mass percentage and density, to determine the required volume for a specific mass of solute.