Problem 18 - Chemistry The Science in Context

Question

How many grams of solute are needed to prepare each of the following solutions? a. \(500.0 \mathrm{mL}\) of \(0.250 M \mathrm{KBr}\) b. \(25.0 \mathrm{mL}\) of \(0.200 M \mathrm{NaNO}_{3}\) c. \(100.0 \mathrm{mL}\) of \(0.375 M \mathrm{CH}_{3} \mathrm{OH}\)

Step-by-Step Solution

Answer

Answer: a. To prepare 500.0 mL of 0.250 M KBr solution, 14.88 g of KBr is needed. b. To prepare 25.0 mL of 0.200 M NaNO3 solution, 0.425 g of NaNO3 is needed. c. To prepare 100.0 mL of 0.375 M CH3OH solution, 1.202 g of CH3OH is needed.

Step 1: Convert volumes to liters

For each solution, we need to convert the given volume in milliliters (mL) to liters (L) using the conversion factor 1 L = 1000 mL. We'll do the conversions in each subsequent step for each solution.

Step 2: Calculate moles of solute for solution a

For solution a, we are given 500.0 mL of 0.250 M KBr. Firstly, convert the volume to liters: Volume (in L) = 500.0 mL × (1 L / 1000 mL) = 0.5 L Now, we can use the formula for molarity to find moles of solute: Moles of solute (KBr) = Molarity × Volume Moles of solute (KBr) = 0.250 M × 0.5 L = 0.125 moles

Step 3: Calculate grams of solute for solution a

Now that we have moles of KBr, we can find the mass using its molar mass (K = 39.10 g/mol and Br = 79.90 g/mol): Molar mass of KBr = 39.10 g/mol + 79.90 g/mol = 119.00 g/mol Mass of solute (KBr) = Moles of solute × Molar mass Mass of solute (KBr) = 0.125 moles × 119.00 g/mol ≈ 14.88 g

Step 4: Calculate moles of solute for solution b

For solution b, we are given 25.0 mL of 0.200 M NaNO3. Firstly, convert the volume to liters: Volume (in L) = 25.0 mL × (1 L / 1000 mL) = 0.025 L Now, we can use the formula for molarity to find moles of solute: Moles of solute (NaNO3) = Molarity × Volume Moles of solute (NaNO3) = 0.200 M × 0.025 L = 0.005 moles

Step 5: Calculate grams of solute for solution b

Now that we have moles of NaNO3, we can find the mass using its molar mass (Na = 22.99 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol): Molar mass of NaNO3 = 22.99 g/mol + 14.01 g/mol + (3 × 16.00 g/mol) = 85.00 g/mol Mass of solute (NaNO3) = Moles of solute × Molar mass Mass of solute (NaNO3) = 0.005 moles × 85.00 g/mol ≈ 0.425 g

Step 6: Calculate moles of solute for solution c

For solution c, we are given 100.0 mL of 0.375 M CH3OH. Firstly, convert the volume to liters: Volume (in L) = 100.0 mL × (1 L / 1000 mL) = 0.1 L Now, we can use the formula for molarity to find moles of solute: Moles of solute (CH3OH) = Molarity × Volume Moles of solute (CH3OH) = 0.375 M × 0.1 L = 0.0375 moles

Step 7: Calculate grams of solute for solution c

Now that we have moles of CH3OH, we can find the mass using its molar mass (C = 12.01 g/mol, H = 1.01 g/mol, and O = 16.00 g/mol): Molar mass of CH3OH = 12.01 g/mol + (3 × 1.01 g/mol) + 16.00 g/mol + 1.01 g/mol = 32.04 g/mol Mass of solute (CH3OH) = Moles of solute × Molar mass Mass of solute (CH3OH) = 0.0375 moles × 32.04 g/mol ≈ 1.202 g So the grams of solute needed for each solution are: a. 14.88 g of KBr b. 0.425 g of NaNO3 c. 1.202 g of CH3OH

Key Concepts

Molarity Calculations

Molarity is a way to express the concentration of a solution. It tells us how many moles of solute are present per liter of solution. To solve a problem using molarity, here’s the typical approach:

• First, convert the volume of solution from milliliters to liters. This is necessary because molarity is defined in terms of liters.
• Next, use the given molarity to calculate moles of solute. The formula is: \[ \text{Moles of solute} = \text{Molarity} \times \text{Volume in liters} \]
• Finally, you use this moles value for further calculations.

This method applies to any scenario where you are given a molarity and volume and need to calculate the amount of solute or other related values.

Mole Conversions

A fundamental chemistry skill is converting between moles and grams. When you know the number of moles of a substance, you can find the mass by using its molar mass. To understand this better, remember:

• Moles represent a count of particles, like atoms or molecules. One mole equals Avogadro’s number, which is approximately \( 6.022 \times 10^{23} \) particles.
• To convert moles to grams, use the molar mass of the substance—this is the mass of one mole of that substance.
• The conversion formula is:\[ \text{Mass in grams} = \text{Moles} \times \text{Molar Mass} \]

Using this method, you can quickly translate between the atomic scale (moles) and the measurable scale (grams). This applies in laboratory settings and in practical problem solving.

Molar Mass Determination

Molar mass is an important concept in chemistry. It combines the atomic masses of each element within a compound to give the mass of one mole of that compound. Here is how you determine it:

• Identify each element in the compound and its quantity. For example, the compound NaNO3 has one sodium, one nitrogen, and three oxygen atoms.
• Look up each element’s atomic mass on the periodic table. For instance, Na = 22.99 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol.
• Add together the atomic masses, multiplied by the number of each type of atom, to get the molar mass.\[\text{Molar Mass of NaNO}_{3} = 22.99 \text{ g/mol} + 14.01 \text{ g/mol} + 3 \times 16.00 \text{ g/mol} = 85.00 \text{ g/mol}\]

Understanding how molar mass is calculated and used is crucial, as it links different properties in chemical equations and daily life applications.