Question

What volume of a \(0.580-M\) solution of \(\mathrm{CaCl}_{2}\) contains 1.28 \(\mathrm{g}\) solute?

Short answer

The volume of the \(0.580-M\) solution of \(\mathrm{CaCl}_{2}\) that contains 1.28 g solute is approximately 19.88 mL.

Step-by-step solution

Calculate the molar mass of CaCl₂

First, we need to find the molar mass of CaCl₂. The molar masses of \(\mathrm{Ca}\), \(\mathrm{Cl}\) are 40.08 g/mol and 35.45 g/mol respectively. So, we can find the molar mass of CaCl₂ as follows: Molar mass of CaCl₂ = (1 × 40.08) + (2 × 35.45) = 40.08 + 70.90 = 110.98 g/mol.

Convert the mass of solute from grams to moles

Now, let's convert the mass of solute (1.28 g) to moles using the molar mass of CaCl₂ (110.98 g/mol). Number of moles = (mass of solute) / (molar mass of CaCl₂) = 1.28 g / 110.98 g/mol = 0.01153 moles

Use the definition of molarity to find the volume of the solution

The definition of molarity (M) is: M = moles of solute / volume of solution (L) We have the molarity of the solution (0.580 M) and the moles of solute (0.01153 moles). Now, we can solve for the volume of the solution (in liters): Volume of solution (L) = moles of solute / molarity = 0.01153 moles / 0.580 M = 0.019876 L

Convert the volume to milliliters

Lastly, we will convert the volume from liters to milliliters for easier reading: Volume of solution (mL) = 0.019876 L × 1000 mL/L = 19.88 mL So, the volume of the 0.580-M solution of CaCl₂ that contains 1.28 g of solute is approximately 19.88 mL.

Key concepts

Molar Mass

Understanding molar mass is essential for solving many chemistry problems. Molar mass refers to the mass of one mole of a given substance. To find it, you sum up the atomic masses of all the atoms in the chemical formula. For example, let's examine calcium chloride, \(\mathrm{CaCl}_{2}\):

1. **Calcium (Ca):** has an atomic mass of 40.08 g/mol.
2. **Chlorine (Cl):** each has an atomic mass of 35.45 g/mol, and since there are two chlorines, you multiply by 2.

The calculation is:

• \( (1 \times 40.08) + (2 \times 35.45) = 40.08 + 70.90 = 110.98\) g/mol.

This gives us the molar mass of \(\mathrm{CaCl}_2\), which helps in converting the mass of a compound to moles, a fundamental step in stoichiometry.

Solution Volume Calculations

Calculating solution volume involves understanding the concept of molarity. Molarity (M) is a measure of concentration, representing the number of moles of solute in one liter of solution. The formula is:

• \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \)

Having the number of moles and the molarity allows you to rearrange the formula to find the solution volume:

• \( \text{Volume (L)} = \frac{\text{moles of solute}}{M} \).

For example, if you have \(0.01153\) moles of \(\mathrm{CaCl}_2\) in a \(0.580-M\) solution, the volume is

• \( \frac{0.01153}{0.580} = 0.019876 \) L, or \(19.88\) mL.

This method allows you to adjust volumes and concentrations depending on the preparation needs.

Stoichiometry

Stoichiometry is a key concept in chemistry involving calculations based on chemical equations. It helps you predict how much product will form from given reactants, or how much reactant is needed to form a desired product amount. Let's break down the steps using our calcium chloride example:1. **Convert Mass to Moles:** Determine the moles of your compound using its molar mass. For \(1.28\) g of \(\mathrm{CaCl}_2\), the moles are:

• \( \frac{1.28}{110.98} = 0.01153 \) moles.

2. **Relate Moles to Molarity:** Using stoichiometry, you can link moles of solute to solution volume using molarity, as shown above.Through these steps, stoichiometry enables precise chemical measurement, ensuring correct proportions in reactions and solutions. This basic understanding is crucial for chemistry, revealing the relationships between substances in a reaction.