Question

Calculate the molarity of each aqueous solution: (a) \(32.3 \mathrm{~g}\) of table sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) in \(100 . \mathrm{mL}\) of solution (b) \(5.80 \mathrm{~g}\) of \(\mathrm{LiNO}_{3}\) in \(505 \mathrm{~mL}\) of solution

Short answer

The molarity of the sugar solution is 0.943 M, and the molarity of the LiNO3 solution is 0.167 M.

Step-by-step solution

Calculate the molar mass

First, determine the molar mass of the solute for each solution. (a) For table sugar \(\text{C}_{12} \text{H}_{22} \text{O}_{11}\)\( \text{C}: 12 \times 12.01 \text{g/mol} = 144.12 \text{g/mol} \text{H}: 22 \times 1.01 \text{g/mol} = 22.22 \text{g/mol} \text{O}: 11 \times 16.00 \text{g/mol} = 176.00 \text{g/mol} \text{Total Molar Mass} = 144.12 + 22.22 + 176.00 = 342.34 \text{g/mol}\)}(b) For \( \text{LiNO}_3\)\( \text{Li}: 6.94 \text{g/mol} \text{N}: 14.01 \text{g/mol} \text{O (3 atoms)}: 3 \times 16.00 \text{g/mol} = 48.00 \text{g/mol} \)\text{Total Molar Mass} = 6.94 + 14.01 + 48.00 = 68.95 \text{g/mol}.

Convert grams to moles

(a) For table sugar, convert grams to moles using its molar mass: \( 32.3 \text{g} \times \frac{1 \text{mol}}{342.34 \text{g}} = 0.0943 \text{mol}\)(b) For \( \text{LiNO}_3\), convert grams to moles: \( 5.80 \text{g} \times \frac{1 \text{mol}}{68.95 \text{g}} = 0.0841 \text{mol}\)

Convert volume to liters

Convert the volume of the solution from milliliters to liters since molarity is expressed in moles per liter.(a) \( 100 \text{mL} = 0.100 \text{L}\)(b) \( 505 \text{mL} = 0.505 \text{L}\)

Calculate molarity

Molarity is calculated by dividing the number of moles of solute by the volume of solution in liters. (a) For table sugar: \( \text{Molarity} (M) = \frac{0.0943 \text{mol}}{0.100 \text{L}} = 0.943 \text{M}\)(b) For \( \text{LiNO}_3\): \( \text{Molarity} (M) = \frac{0.0841 \text{mol}}{0.505 \text{L}} = 0.167 \text{M}\)

Key concepts

Molar Mass

Molar mass is a key concept in chemistry. It represents the mass of one mole of a given substance. To calculate it, you need to add up the atomic masses of all the atoms in a molecule. For example, let's take table sugar (C₁₂H₂₂O₁₁). Every hydrogen atom has an atomic mass of about 1.01 g/mol, oxygen approximately 16 g/mol, and carbon around 12.01 g/mol. Multiplying these atomic masses by the number of atoms present in the molecule, we get:

• Carbon: 12 atoms * 12.01 g/mol = 144.12 g/mol
• Hydrogen: 22 atoms * 1.01 g/mol = 22.22 g/mol
• Oxygen: 11 atoms * 16.00 g/mol = 176.00 g/mol

Adding these values together gives us the molar mass of table sugar, which is 342.34 g/mol. Similarly, for lithium nitrate (LiNO₃), you need to add up the molar masses of lithium, nitrogen, and oxygen to get 68.95 g/mol.

Moles to Grams Conversion

To convert grams to moles, you use the molar mass of the substance. This is helpful when you have a certain mass of a compound and need to determine how many moles it represents. The formula for this conversion is: \[ \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass}} \]For instance, if you have 32.3 grams of table sugar and you know the molar mass is 342.34 g/mol, the calculation would be:\[ 32.3 \text{ g} \times \frac{1 \text{ mol}}{342.34 \text{ g}} = 0.0943 \text{ mol} \]Similarly, if you have 5.80 grams of LiNO₃, using its molar mass of 68.95 g/mol, you would get:\[ 5.80 \text{ g} \times \frac{1 \text{ mol}}{68.95 \text{ g}} = 0.0841 \text{ mol} \]

Solution Volume Conversion

When calculating molarity, you need the volume in liters, as molarity is expressed in moles per liter. Therefore, converting milliliters to liters becomes necessary. To convert, use the formula:\[ \text{Volume in liters} = \text{Volume in milliliters} \times \frac{1}{1000} \]For example, 100 mL is equivalent to 0.100 L, as seen in step 3 of the solution. Similarly, 505 mL converts to 0.505 L. These conversions ensure your molarity calculations are accurate and in the proper units.

Molar Concentration Calculation

Molar concentration, or molarity, quantifies concentration by the number of moles of solute per liter of solution. The formula to calculate molarity is:\[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]Take the example of table sugar: if you have 0.0943 moles of it dissolved in 0.100 liters of solution, the molarity is calculated as:\[ \text{Molarity} (M) = \frac{0.0943 \text{ mol}}{0.100 \text{ L}} = 0.943 \text{ M} \]Similarly, for LiNO₃, if you have 0.0841 moles of it in 0.505 liters, the molarity is:\[ \text{Molarity} (M) = \frac{0.0841 \text{ mol}}{0.505 \text{ L}} = 0.167 \text{ M} \]Understanding these steps is fundamental in preparing solutions of desired concentrations.