A solution is prepared with 70.0 g of HNO₃ and 130.0 g of H₂O. The HNO₃ solution has a density of 1.21 g/mL.
b. What is the total volume, in milliliters, of the solution?

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the total volume of the solution in milliliters. The solution is made by mixing 70.0 g of HNO₃ and 130.0 g of H₂O, and the density of the solution is given as 1.21 g/mL.
2. Step 2: Calculate the total mass of the solution. Add the mass of HNO₃ and the mass of H₂O: $m$_total = 70.0 + 130.0 = 200.0 g.
3. Step 3: Use the formula for density to calculate the volume of the solution. The formula is $d=\frac{m}{V}$, where $d$ is the density, $m$ is the mass, and $V$ is the volume. Rearrange the formula to solve for volume: $V=\frac{m}{d}$.
4. Step 4: Substitute the known values into the formula. Use the total mass of the solution ($200.0g$) and the density of the solution ($1.21g/\mathrm{mL}$): $V=\frac{200.0}{1.21}$.
5. Step 5: Perform the division to find the volume in milliliters. The result will give you the total volume of the solution in mL.

Key Concepts

Density

Density is defined as mass per unit volume, typically expressed in grams per milliliter (g/mL) for liquids. It is a crucial property that helps determine how much space a given mass of a substance will occupy. In this question, the density of the HNO₃ solution is provided, which allows us to calculate the volume of the solution using the formula: Volume = Mass / Density.

Mass of the Solution

The total mass of the solution is the sum of the masses of its components. In this case, it includes the mass of HNO₃ (70.0 g) and the mass of water (130.0 g). Understanding the total mass is essential for calculating the overall volume of the solution, as it directly influences the density and the resulting volume when combined with the density value.

Volume Calculation

Volume calculation involves using the relationship between mass, density, and volume to find the total volume of a solution. The formula used is Volume = Mass / Density. By applying this formula to the total mass of the solution and the given density, one can determine the total volume in milliliters, which is the final goal of the question.