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. (9.4)d. What is the molarity (M) of the solution?

Verified step by step guidance

1. Calculate the number of moles of HNO₃ using its molar mass. The molar mass of HNO₃ is approximately 63.01 g/mol. Use the formula: \( \text{moles of HNO₃} = \frac{\text{mass of HNO₃}}{\text{molar mass of HNO₃}} \).
2. Determine the total mass of the solution by adding the mass of HNO₃ and the mass of H₂O: \( \text{total mass} = 70.0 \text{ g} + 130.0 \text{ g} \).
3. Calculate the volume of the solution using its density. Use the formula: \( \text{volume} = \frac{\text{total mass}}{\text{density}} \), where the density is given as 1.21 g/mL.
4. Convert the volume from mL to L, since molarity is expressed in moles per liter. Use the conversion: \( 1 \text{ L} = 1000 \text{ mL} \).
5. Calculate the molarity (M) of the solution using the formula: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).

Key Concepts

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. It is calculated using the formula M = moles of solute / volume of solution in liters. Understanding molarity is essential for determining how concentrated a solution is, which is crucial in various chemical reactions and applications.

Calculating Moles

To find the molarity, one must first calculate the number of moles of the solute, in this case, HNO₃. This is done using the formula: moles = mass (g) / molar mass (g/mol). The molar mass of HNO₃ is approximately 63.01 g/mol, and knowing how to convert grams to moles is fundamental for solving molarity problems.

Volume of Solution

The volume of the solution is necessary to calculate molarity and can be determined from the mass and density of the solution. The formula for volume is volume = mass / density. In this scenario, the total mass of the solution (HNO₃ + H₂O) and the given density allow for the calculation of the solution's volume, which is critical for the final molarity calculation.