Question

Calculate the weight of \(\mathrm{CO}_{2}\), which occupies a volume of \(11.2 \mathrm{dm}^{3}\) at STP.

Short answer

Answer: The weight of CO₂ gas occupying a volume of 11.2 dm³ at STP is 22.51 g.

Step-by-step solution

Calculate the number of moles using the volume of CO₂ at STP

To find the number of moles, we can use the equation: n = \(\frac{V}{V_m}\) Where, n is the number of moles, V is the given volume and \(V_m\) is the molar volume of the gas at STP conditions. For an ideal gas, the molar volume at STP is \(22.4\mathrm{dm^{3}mol^{-1}}\). Substitute the given values into the equation: n = \(\frac{11.2}{22.4}\) Calculate the number of moles of CO₂: n = \(0.5\) moles

Determine the molar mass of CO₂

The chemical formula for CO₂ is \(\mathrm{CO}_{2}\). So, we need to calculate the molar mass of one carbon atom and two oxygen atoms. Recall that the atomic masses of Carbon (C) and Oxygen (O) are \(12.01\,\mathrm{g\,mol^{-1}}\) and \(16.00\,\mathrm{g\,mol^{-1}}\) respectively. Therefore, the molar mass of CO₂ can be calculated as follows: Molar mass of CO₂ = (1 × molar mass of C) + (2 × molar mass of O) Molar mass of CO₂ = (1 × \(12.01\,\mathrm{g\,mol^{-1}}\)) + (2 × \(16.00\,\mathrm{g\,mol^{-1}}\)) Molar mass of CO₂ = \(45.01\,\mathrm{g\,mol^{-1}}\)

Calculate the weight of CO₂

Now we have the number of moles (n = 0.5 moles) and the molar mass of CO₂ (\(45.01\,\mathrm{g\,mol^{-1}}\)). To find the weight of CO₂, multiply the number of moles by the molar mass: Weight of CO₂ = n × molar mass of CO₂ Weight of CO₂ = \(0.5\,\text{moles} × 45.01\,\mathrm{g\,mol^{-1}}\) Calculate the weight of CO₂: Weight of CO₂ = \(22.51\,\mathrm{g}\) Hence, the weight of \(\mathrm{CO}_{2}\) occupying a volume of \(11.2\,\mathrm{dm^{3}}\) at STP is \(22.51\,\mathrm{g}\).