Question

(a) Define molarity. (b) Calculate the molarity of sodium carbonate solution containing \(0.53 \mathrm{~g}\) of sodium carbonate dissolved in \(200 \mathrm{ml}\) of the solution.

Short answer

Answer: The molarity of the sodium carbonate solution is 0.025 M.

Step-by-step solution

Define molarity

Molarity (M) is defined as the number of moles of solute (e.g., sodium carbonate) dissolved per liter of solution. Mathematically, it can be expressed as: Molarity (M) = \(\frac{\text{moles of solute}}{\text{volume of solution (in liters)}}\)

Calculate moles of sodium carbonate

To calculate the moles of sodium carbonate (Na2CO3), we will use the formula: Moles = \(\frac{\text{mass}}{\text{molar mass}}\) The molar mass of Na2CO3 is 22.99 (for 2 Na) + 12.01 (for C) + 16.00 (for 3 O) = 105.99 grams/mol Given the mass of sodium carbonate as 0.53 g, we can calculate the moles of sodium carbonate: Moles of Na2CO3 = \(\frac{0.53 \text{ g}}{105.99 \text{ g/mol}} \approx 0.005 \text{ mol}\)

Convert volume of solution to liters

The volume of the solution is given as 200 ml. To convert it to liters, we use the conversion factor: 1 L = 1000 ml. Volume of solution in liters = \(\frac{200 \text{ ml}}{1000 \mathrm{~ml/L}} = 0.2 \mathrm{~L}\)

Calculate molarity of the solution

Now that we have the moles of solute (sodium carbonate) and the volume of the solution in liters, we can calculate the molarity of the solution: Molarity of Na2CO3 solution = \(\frac{0.005 \mathrm{~mol}}{0.2 \mathrm{~L}}= 0.025 \mathrm{~M}\) So, the molarity of the sodium carbonate solution is 0.025 M.