Question

(a) How many grams of solute are present in \(50.0 \mathrm{~mL}\) of \(0.488 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} ?\) (b) If \(4.00 \mathrm{~g}\) of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) is dissolved in enough water to form \(400 \mathrm{~mL}\) of solution, what is the molarity of the solution? (c) How many milliliters of \(0.0250 \mathrm{M} \mathrm{CuSO}_{4}\) contain \(1.75 \mathrm{~g}\) of solute?

Short answer

(a) There are 7.17 g of solute (K2Cr2O7) in 50.0 mL of 0.488 M K2Cr2O7 solution. (b) The molarity of the solution with 4.00 g of (NH4)2SO4 dissolved in 400 mL of water is 0.0758 M. (c) 438.8 mL of 0.0250 M CuSO4 solution contains 1.75 g of solute.

Step-by-step solution

Problem (a): Find grams of solute in 50.0 mL of 0.488 M K2Cr2O7 solution

First, we must recall the definition of molarity (M): the number of moles of solute per liter of solution. We are given the volume (50.0 mL) and molarity (0.488 M) of the K2Cr2O7 solution and asked to find the mass of K2Cr2O7. We can use the following steps: 1. Convert volume from mL to L 2. Determine the number of moles of solute using molarity and volume 3. Convert moles of solute to grams using the molar mass of K2Cr2O7 Step 1: Convert volume from mL to L We are given a volume of 50.0 mL. To convert it to liters, divide by 1000: \(50.0\,\mathrm{mL} \cdot \frac{1\,\mathrm{L}}{1000\,\mathrm{mL}} = 0.0500\,\mathrm{L}\) Step 2: Determine the number of moles of solute using molarity and volume We know the molarity of the solution is 0.488 M. Thus: \(\text{moles of K}_{2}\text{Cr}_{2}\text{O}_{7} = \text{molarity} \times \text{volume} = 0.488\,\text{M} \times 0.0500\,\text{L} = 0.0244\,\text{moles}\) Step 3: Convert moles of solute to grams using the molar mass of K2Cr2O7 The molar mass of K2Cr2O7 is approximately 294.2 g/mol. To find the mass in grams: \(\text{grams of K}_{2}\text{Cr}_{2}\text{O}_{7} = \text{moles} \times \text{molar mass} = 0.0244\,\text{moles} \times 294.2\,\frac{\text{g}}{\text{mol}} = 7.17\,\text{g}\) So there are 7.17 grams of solute (K2Cr2O7) in 50.0 mL of 0.488 M K2Cr2O7 solution.

Problem (b): Find molarity of the solution with 4.00 g of (NH4)2SO4 dissolved in 400 mL of water

We are given the mass of solute (4.00 g) and volume of solution (400 mL) and asked to find the molarity. We can use the following steps: 1. Convert mass of solute to moles using the molar mass of (NH4)2SO4 2. Convert volume of solution from mL to L 3. Determine the molarity using moles of solute and volume of solution Step 1: Convert mass of solute to moles using the molar mass of (NH4)2SO4 The molar mass of (NH4)2SO4 is approximately 132.1 g/mol. To find the number of moles: \(\text{moles of (NH}_{4}\text{)}_{2}\text{SO}_{4} = \frac{\text{mass}}{\text{molar mass}} = \frac{4.00\,\text{g}}{132.1\,\frac{\text{g}}{\text{mol}}} = 0.0303\,\text{moles}\) Step 2: Convert volume of solution from mL to L We are given a volume of 400 mL. To convert it to liters, divide by 1000: \(400\,\mathrm{mL} \cdot \frac{1\,\mathrm{L}}{1000\,\mathrm{mL}} = 0.400\,\mathrm{L}\) Step 3: Determine the molarity using moles of solute and volume of solution \(\text{molarity} = \frac{\text{moles of solute}}{\text{volume of solution}} = \frac{0.0303\,\text{moles}}{0.400\,\text{L}} = 0.0758\,\text{M}\) So the molarity of the solution is 0.0758 M.

Problem (c): Find volume (in mL) of 0.0250 M CuSO4 solution containing 1.75 g of solute

We are given the mass of solute (1.75 g) and the molarity of the solution (0.0250 M) and asked to find the volume of the solution in mL. We can use the following steps: 1. Convert mass of solute to moles using the molar mass of CuSO4 2. Determine the volume of solution using moles of solute and molarity 3. Convert volume of solution from L to mL Step 1: Convert mass of solute to moles using the molar mass of CuSO4 The molar mass of CuSO4 is approximately 159.6 g/mol. To find the number of moles: \(\text{moles of CuSO}_{4} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.75\,\text{g}}{159.6\,\frac{\text{g}}{\text{mol}}} = 0.01097\,\text{moles}\) Step 2: Determine the volume of solution using moles of solute and molarity \(\text{volume of solution} = \frac{\text{moles of solute}}{\text{molarity}} = \frac{0.01097\,\text{moles}}{0.0250\,\text{M}} = 0.4388\,\text{L}\) Step 3: Convert volume of solution from L to mL \(0.4388\,\mathrm{L} \cdot \frac{1000\,\mathrm{mL}}{1\,\mathrm{L}} = 438.8\,\mathrm{mL}\) So, 438.8 mL of 0.0250 M CuSO4 solution contains 1.75 g of solute.

Key concepts

Molarity Definition

Molarity is a fundamental concept in chemistry that refers to the concentration of a solution. It's denoted as M and defined as the number of moles of solute per liter of solution.

To put it simply, molarity tells us how 'strong' or 'concentrated' a solution is. The higher the molarity, the more solute there is in a given volume of solution. When solving problems involving molar concentration, understanding this concept is crucial.

Moles to Grams Conversion

When working with chemical solutions, it's often necessary to switch between the mass of a substance in grams and the amount of substance in moles. This is where the concept of molar mass comes into play.

The molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). To convert moles to grams, you multiply the number of moles by the molar mass of the substance. Conversely, to find the number of moles from grams, you divide the mass by the molar mass.

These calculations are a keystone of solution preparation and molarity calculations since they link the measurable mass of a substance to its number of particles, represented by moles.

Solution Preparation

Preparing a solution with a specific molarity requires careful calculation and measurement. First, the desired molarity is determined, and then, the amount of solute needed is calculated, either by moles or mass, depending on the information available. After measuring out the solute, it's dissolved in a suitable volume of solvent to achieve the desired concentration.

It's vital to note that one should add the solute to less solvent than needed, dissolve it completely, and then carefully dilute to the final volume. This ensures that the concentration of the solution is accurate and consistent with the required molarity.