Question

What is the molarity of the following solutions? (a) \(12.5 \mathrm{~g} \mathrm{NaHCO}_{3}\) in \(350.0 \mathrm{~mL}\) solution (b) \(45.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{SO}_{4}\) in \(300.0 \mathrm{~mL}\) solution (c) \(30.0 \mathrm{~g} \mathrm{NaCl}\) dissolved to make \(500.0 \mathrm{~mL}\) solution

Short answer

(a) 0.425 M, (b) 1.53 M, (c) 1.026 M.

Step-by-step solution

Understanding Molarity

Molarity is defined as the number of moles of solute per liter of solution. The formula for molarity \( M \) is: \[ M = \frac{n}{V} \] where \( n \) is the number of moles of solute and \( V \) is the volume of the solution in liters.

Calculate Moles of Solute

First, calculate the number of moles \( n \) for each solute using the formula: \[ n = \frac{ ext{mass}}{ ext{molar mass}} \] where mass is the given mass of the solute in grams and molar mass is the molar mass of the solute in grams per mole.

Step 3(a): Calculate Moles of NaHCO₃

Find the molar mass of \( \mathrm{NaHCO}_3 \):* \( \mathrm{Na} = 23.0 \mathrm{~g/mol} \)* \( \mathrm{H} = 1.0 \mathrm{~g/mol} \)* \( \mathrm{C} = 12.0 \mathrm{~g/mol} \)* \( 3 \times \mathrm{O} = 3 \times 16.0 \mathrm{~g/mol} = 48.0 \mathrm{~g/mol} \)Total Molar Mass = 84.0 g/mol.Calculate moles: \[ n = \frac{12.5 \mathrm{~g}}{84.0 \mathrm{~g/mol}} = 0.1488 \mathrm{~mol} \]

Step 4(a): Calculate Molarity for NaHCO₃ Solution

Convert volume from mL to L: 350.0 mL = 0.350 L.Use the molarity formula: \[ M = \frac{0.1488 \mathrm{~mol}}{0.350 \mathrm{~L}} = 0.425 \mathrm{~M} \].

Step 3(b): Calculate Moles of H₂SO₄

Find the molar mass of \( \mathrm{H}_2\mathrm{SO}_4 \):* \( 2 \times \mathrm{H} = 2 \times 1.0 \mathrm{~g/mol} = 2.0 \mathrm{~g/mol} \)* \( \mathrm{S} = 32.1 \mathrm{~g/mol} \)* \( 4 \times \mathrm{O} = 4 \times 16.0 \mathrm{~g/mol} = 64.0 \mathrm{~g/mol} \)Total Molar Mass = 98.1 g/mol.Calculate moles: \[ n = \frac{45.0 \mathrm{~g}}{98.1 \mathrm{~g/mol}} = 0.459 \mathrm{~mol} \]

Step 4(b): Calculate Molarity for H₂SO₄ Solution

Convert volume from mL to L: 300.0 mL = 0.300 L.Use the molarity formula: \[ M = \frac{0.459 \mathrm{~mol}}{0.300 \mathrm{~L}} = 1.53 \mathrm{~M} \].

Step 3(c): Calculate Moles of NaCl

Find the molar mass of \( \mathrm{NaCl} \):* \( \mathrm{Na} = 23.0 \mathrm{~g/mol} \)* \( \mathrm{Cl} = 35.5 \mathrm{~g/mol} \)Total Molar Mass = 58.5 g/mol.Calculate moles: \[ n = \frac{30.0 \mathrm{~g}}{58.5 \mathrm{~g/mol}} = 0.513 \mathrm{~mol} \]

Step 4(c): Calculate Molarity for NaCl Solution

Convert volume from mL to L: 500.0 mL = 0.500 L.Use the molarity formula: \[ M = \frac{0.513 \mathrm{~mol}}{0.500 \mathrm{~L}} = 1.026 \mathrm{~M} \].

Key concepts

Moles of Solute

Understanding how to calculate the moles of a solute is essential in chemistry, especially for determining the molarity of a solution. Moles represent the number of specified atoms, ions or molecules in a substance. This count is based on the fixed quantity called Avogadro's number, which is approximately \( 6.022 \times 10^{23} \). This exact count helps make sense of chemical reactions and stoichiometry.
To find the number of moles in a given mass of a solute, you can use the formula:

• Formula: \( n = \frac{\text{mass}}{\text{molar mass}} \)
• Mass: The weight of the solute you have, usually in grams.
• Molar Mass: The weight of one mole of your substance, often given in grams per mole (g/mol).

For example, if you have 12.5 grams of sodium bicarbonate (\(\mathrm{NaHCO}_3\)), with a molar mass of 84 g/mol, the number of moles is given by: \[ n = \frac{12.5 \text{ g}}{84 \text{ g/mol}} = 0.1488 \text{ mol} \] Knowing the precise moles helps you proceed with calculating the actual molarity of the solution.

Solution Volume

Volume in chemistry often refers to the space that a solution occupies. In the context of molarity calculations, it's crucial to understand that the volume of a solution affects the concentration. Molarity, defined as moles of solute per liter of solution, requires volume to be in liters to maintain consistency across calculations.
Whenever you're calculating molarity, if your solution's volume is given in milliliters (mL), you'll need to convert that value into liters. This is an essential step because molarity uses liters as its standard unit of measurement for solution volumes.

• Conversion: To convert mL to L, divide the volume in mL by 1000.
• Example: 350 mL = 0.350 L

For our examples, if you dissolve solute in 350 mL of solution, you will convert it to liters by performing: \[ 350.0 \text{ mL} = 0.350 \text{ L} \]This converted volume (now in liters) can be directly used in the molarity formula to calculate the concentration of the solution.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is an intrinsic property of compounds and is crucial for converting between grams and moles. Calculating molar mass involves summing the atomic masses of all atoms in a compound's formula.
The atomic masses of elements are typically found on the periodic table, and these values give insight into how much one mole of any element or compound weighs. For instance:

• For \(\mathrm{NaHCO}_3\), the molar mass calculation is:
  • Sodium (Na): 23.0 g/mol
  • Hydrogen (H): 1.0 g/mol
  • Carbon (C): 12.0 g/mol
  • Oxygen (O): 16.0 g/mol (and multiply by 3 for \(\mathrm{O}\_3\))
• Thus, the total molar mass of \(\mathrm{NaHCO}_3\) becomes \[ 23.0 + 1.0 + 12.0 + 48.0 = 84.0 \text{ g/mol} \]

The molar mass acts as a bridge to convert a given mass of a substance to the number of moles. This conversion is foundational in chemistry for making accurate calculations and comparisons during chemical experimentation and analysis.