Dry ice (solid carbon dioxide) has a density of 1.35 g/mL. If 25.0 mL of dry ice is placed inside an empty balloon and completely sublimes to gaseous carbon dioxide, then what is the balloon’s volume at STP? Assume the balloon was sealed after the solid CO2 was added.
The Correct Answer and Explanation is :
When 25.0 mL of dry ice (solid carbon dioxide) is placed inside a sealed balloon and completely sublimes to gaseous CO₂ at standard temperature and pressure (STP), the balloon’s volume can be calculated as follows:
- Calculate the mass of the dry ice: Given the density of dry ice is 1.35 g/mL, the mass (m) of 25.0 mL is: [ m = \text{density} \times \text{volume} = 1.35\, \text{g/mL} \times 25.0\, \text{mL} = 33.75\, \text{g} ]
- Determine the number of moles of CO₂: The molar mass of CO₂ is approximately 44.01 g/mol. The number of moles (n) is: [ n = \frac{\text{mass}}{\text{molar mass}} = \frac{33.75\, \text{g}}{44.01\, \text{g/mol}} \approx 0.767\, \text{mol} ]
- Calculate the volume of CO₂ gas at STP: At STP (0°C and 1 atm), one mole of an ideal gas occupies approximately 22.414 liters. Thus, the volume (V) of 0.767 moles of CO₂ is: [ V = n \times \text{molar volume} = 0.767\, \text{mol} \times 22.414\, \text{L/mol} \approx 17.2\, \text{L} ]
Explanation:
Dry ice is the solid form of carbon dioxide (CO₂). When placed in a sealed balloon, it sublimes directly from solid to gas without passing through a liquid phase. The density of dry ice allows us to calculate its mass based on the given volume. Using the molar mass of CO₂, we determine the number of moles present. At STP, the molar volume of an ideal gas is approximately 22.414 L/mol, which enables us to calculate the total volume the CO₂ gas would occupy. Therefore, the balloon’s volume at STP would be approximately 17.2 liters.