Problem 44 - Chemistry The Molecular Science

Question

Calculate the mass in grams of solute required to prepare each of these solutions. (a) \(750 \cdot \mathrm{mL}\) of \(4.00-\mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) (b) \(1.50 \mathrm{~L}\) of \(0.750-\mathrm{M} \mathrm{KCl}\) (c) \(150 . \mathrm{mL}\) of \(0.350-\mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

(a) 160.47 g NH4Cl, (b) 83.37 g KCl, (c) 7.46 g Na2SO4

Step 1: Understanding Molarity

Molarity (M) is the number of moles of solute per liter of solution. Formula: \( M = \frac{n}{V} \) where \( n \) is moles of solute and \( V \) is volume in liters.

Step 2: Converting Volume to Liters (Part a)

For 750 mL, convert to liters: \( V = \frac{750}{1000} = 0.750 \) L.

Step 3: Calculate Moles of NH4Cl (Part a)

Using \( 4.00 \) M, calculate moles: \( n = MV = 4.00 \times 0.750 = 3.00 \) moles.

Step 4: Calculate Mass of NH4Cl (Part a)

Molar mass of \( \mathrm{NH}_{4} \mathrm{Cl} \) is \( 53.49 \) g/mol. Mass = \( 3.00 \times 53.49 = 160.47 \) g.

Step 5: Converting Volume to Liters (Part b)

For 1.50 L, no conversion is needed; volume is already in liters.

Step 6: Calculate Moles of KCl (Part b)

Using \( 0.750 \) M, calculate moles: \( n = MV = 0.750 \times 1.50 = 1.125 \) moles.

Step 7: Calculate Mass of KCl (Part b)

Molar mass of \( \mathrm{KCl} \) is \( 74.55 \) g/mol. Mass = \( 1.125 \times 74.55 = 83.36875 \) g.

Step 8: Converting Volume to Liters (Part c)

For 150 mL, convert to liters: \( V = \frac{150}{1000} = 0.150 \) L.

Step 9: Calculate Moles of Na2SO4 (Part c)

Using \( 0.350 \) M, calculate moles: \( n = MV = 0.350 \times 0.150 = 0.0525 \) moles.

Step 10: Calculate Mass of Na2SO4 (Part c)

Molar mass of \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) is \( 142.04 \) g/mol. Mass = \( 0.0525 \times 142.04 = 7.4561 \) g.

Key Concepts

Moles of Solute

Understanding the concept of moles is crucial in chemistry, especially when preparing solutions. A mole is a unit that measures the amount of a substance. It's like a dozen for eggs but in the scale of atoms, molecules, and ions.
A mole of any substance always contains Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\). This is an incredibly large number, which makes it a handy unit for counting tiny particles.
When you calculate molarity, you're determining how many moles of solute are present in one liter of solution. You can find the moles () using the formula: (Molarity \(M\)) by (Volume \(V\) in liters), i.e., \( n = MV \).
For instance, if you have 4.00 M of \( \mathrm{NH}_{4} \mathrm{Cl}\) in 0.750 L of solution, you multiply them to find the moles: \(4.00 \times 0.750 = 3.00\) moles.

Molar Mass

Molar mass is a central concept in chemistry that links the mass of a substance to the number of moles it contains. It is defined as the mass of one mole of a substance, expressed in grams per mole (g/mol).
Molar mass is obtained by summing the atomic masses of all the atoms in a molecule. These atomic masses are found on the periodic table and are expressed in atomic mass units (amu). For example, the molar mass of \( \mathrm{NH}_{4}\mathrm{Cl} \) is calculated by adding the atomic masses of nitrogen (N), hydrogen (H), and chlorine (Cl), which results in 53.49 g/mol.
Knowing the molar mass is essential when you need to calculate the mass of a solute in grams. Once you know how many moles of a substance are needed, you simply multiply by the molar mass to find the mass in grams. For example, for \( \mathrm{NH}_{4}\mathrm{Cl} \), if you determined you need 3.00 moles, you multiply by its molar mass to get the mass: \( 3.00 \text{ moles} \times 53.49 \text{ g/mol} = 160.47 \text{ grams} \).

Solution Preparation

Preparing a solution accurately is a vital skill in chemistry, and it involves several steps. It starts with understanding the desired concentration and volume of your solution.
First, determine the volume of the solution in liters, as molarity is expressed in moles per liter. Convert milliliters to liters by dividing the volume in mL by 1000.
Next, calculate the moles of solute needed using the formula \( n = MV \), where \( M \) is the molarity, and \( V \) is the volume in liters.
Once you have the number of moles, use the molar mass to find the required mass of the solute. After calculating the mass, measure that amount of solute using a balance.
Dissolve the solute in a volume of solvent that is less than the target volume. Once dissolved, dilute the solution to the final desired volume. This ensures precision in the concentration of the solution.
By carefully following these steps, you ensure the solution is prepared correctly, which is crucial for accurate and reliable experimental results.