Reacting masses and volumes (of solutions and gases) — practice questions

Step 1: Calculate the molar mass of $CaCO_3$. \ $M_r(CaCO_3) = 40.1 + 12.0 + (3 \times 16.0) = 100.1 \text{ g mol}^{-1}$ \ Step 2: Calculate the moles of $CaCO_3$. \ $n(CaCO_3) = \frac{m}{M_r} = \frac{5.00}{100.1} = 0.04995 \text{ mol}$ \ Step 3: Use the mole ratio from the balanced equation. \ The ratio of $CaCO_3 : CO_2$ is 1:1. \ Therefore, $n(CO_2) = n(CaCO_3) = 0.04995 \text{ mol}$. \ Step 4: Calculate the volume of $CO_2$ gas. \ Volume of $CO_2$ (in dm³) = $n \times 24 = 0.04995 \times 24 = 1.1988 \text{ dm}^3$. \ Step 5: Convert the volume to cm³. \ Volume in cm³ = $1.1988 \times 1000 = 1198.8 \text{ cm}^3$. \ Final Answer (to 3 s.f.): $1200 \text{ cm}^3$.

Step 1: Calculate the moles of the known substance ($H_2SO_4$). \ Volume of $H_2SO_4 = \frac{22.50}{1000} = 0.02250 \text{ dm}^3$. \ $n(H_2SO_4) = c \times V = 0.0500 \text{ mol dm}^{-3} \times 0.02250 \text{ dm}^3 = 0.001125 \text{ mol}$. \ Step 2: Use the mole ratio to find the moles of the unknown substance (NaOH). \ From the equation, the ratio $NaOH : H_2SO_4$ is 2:1. \ Therefore, $n(NaOH) = 2 \times n(H_2SO_4) = 2 \times 0.001125 = 0.002250 \text{ mol}$. \ Step 3: Calculate the concentration of the unknown substance (NaOH). \ Volume of $NaOH = \frac{25.0}{1000} = 0.0250 \text{ dm}^3$. \ $c(NaOH) = \frac{n}{V} = \frac{0.002250 \text{ mol}}{0.0250 \text{ dm}^3} = 0.0900 \text{ mol dm}^{-3}$. \ Final Answer: $0.0900 \text{ mol dm}^{-3}$.