Question

How many moles and how many grams of the indicated solute does each of the following solutions contain? a. 4.25 L of \(0.105 M\) KCl solution b. \(15.1 \mathrm{mL}\) of \(0.225 \mathrm{M} \mathrm{NaNO}_{3}\) solution c. \(25 \mathrm{mL}\) of \(3.0 \mathrm{M} \mathrm{HCl}\) d. \(100 .\) mL of \(0.505 M \mathrm{H}_{2} \mathrm{SO}_{4}\)

Short answer

a. 4.25 L of 0.105 M KCl solution contains 0.44625 mol and 33.29 g of KCl. b. 15.1 mL of 0.225 M NaNO3 solution contains 0.0034025 mol and 0.28921 g of NaNO3. c. 25 mL of 3.0 M HCl contains 0.075 mol and 2.7345 g of HCl. d. 100 mL of 0.505 M H2SO4 contains 0.0505 mol and 4.95454 g of H2SO4.

Step-by-step solution

Calculate moles of solute

Moles of KCl = Molarity × Volume Moles of KCl = \(0.105 \mathrm{M}\) × \(4.25 \mathrm{L}\) Moles of KCl = 0.44625 mol

Convert moles to grams

Molar mass of KCl = 39.10 g/mol (K) + 35.45 g/mol (Cl) = 74.55 g/mol Grams of KCl = moles × molar mass Grams of KCl = 0.44625 mol × 74.55 g/mol Grams of KCl = 33.29 g b. 15.1 mL of 0.225 M NaNO3 solution

Calculate moles of solute

Moles of NaNO3 = Molarity × Volume (convert mL to L) Moles of NaNO3 = 0.225 M × 0.0151 L Moles of NaNO3 = 0.0034025 mol

Convert moles to grams

Molar mass of NaNO3 = 22.99 g/mol (Na) + 14.01 g/mol (N) + 3 × 16 g/mol (O) = 85 g/mol Grams of NaNO3 = moles × molar mass Grams of NaNO3 = 0.0034025 mol × 85 g/mol Grams of NaNO3 = 0.28921 g c. 25 mL of 3.0 M HCl

Calculate moles of solute

Moles of HCl = Molarity × Volume (convert mL to L) Moles of HCl = 3.0 M × 0.025 L Moles of HCl = 0.075 mol

Convert moles to grams

Molar mass of HCl = 1.01 g/mol (H) + 35.45 g/mol (Cl) = 36.46 g/mol Grams of HCl = moles × molar mass Grams of HCl = 0.075 mol × 36.46 g/mol Grams of HCl = 2.7345 g d. 100 mL of 0.505 M H2SO4

Calculate moles of solute

Moles of H2SO4 = Molarity × Volume (convert mL to L) Moles of H2SO4 = 0.505 M × 0.1 L Moles of H2SO4 = 0.0505 mol

Convert moles to grams

Molar mass of H2SO4 = 2 × 1.01 g/mol (H) + 32.07 g/mol (S) + 4 × 16 g/mol (O) = 98.09 g/mol Grams of H2SO4 = moles × molar mass Grams of H2SO4 = 0.0505 mol × 98.09 g/mol Grams of H2SO4 = 4.95454 g

Key concepts

Calculating Moles

Moles measure the amount of a substance. Think of it like counting the number of molecules or atoms in a sample. The formula used to calculate moles in a solution is fairly straightforward. You multiply the molarity (\( M \)) by the volume of the solution (\( L \)). Here's the key formula:
\[ \text{Moles} = \text{Molarity} \times \text{Volume in Liters} \]To successfully perform this calculation, remember to:

• Always convert volume measurements to liters if they're not already. For instance, dividing milliliters by 1000 converts them into liters.
• The molarity, \(M\), tells you how many moles of solute are in one liter of solution.

Applying this formula helps in various chemical calculations, like figuring out how much of a compound is present in your solution.

Converting Moles to Grams

Once you know how many moles of a substance you have, you often need to convert this value to grams. This conversion helps understand how much of a substance you physically have by using its molar mass. The formula to convert moles to grams is:
\[ \text{Grams} = \text{Moles} \times \text{Molar Mass} \]Key steps include:

• Know the molar mass of your substance. This is typically available from the periodic table and gives you the mass of one mole of a substance.
• Simply multiply the number of moles by the molar mass.

This conversion is essential, especially in lab settings, where precise amounts are necessary for reactions and experiments.

Molar Mass

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. It's typically expressed in terms of grams per mole (\(g/mol\)). To find the molar mass:

• Add up the atomic masses of all atoms in a molecule. Use a periodic table for this data.
• For example, to find the molar mass of potassium chloride (KCl), you add the atomic mass of potassium (\(39.10\ g/mol\)) and chlorine (\(35.45\ g/mol\)), which equals \(74.55\ g/mol\).

Understanding molar mass is important for converting between grams and moles, ensuring accurate chemical experimentation and analysis. This knowledge simplifies dosing, reaction measurements, and understanding the proportion of elements in compounds.