Final answer:
To calculate the density of a sample of H₂O gas, use the ideal gas law equation PV = nRT. Convert the given temperature and pressure to Kelvin and kPa, respectively. Rearrange the equation to solve for density, and divide the mass by the volume to obtain the density in g/cm³. The correct answer is A. 0.5 g/L.
Step-by-step explanation:
To calculate the density of a sample of H₂O gas at a given temperature and pressure, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. To find the density, we need to rearrange the equation to solve for density. Density is equal to the mass divided by the volume.
In this case, we don't have the mass, but we can use the molar mass of water (18.015 g/mol) to find the mass. Once we calculate the volume of the sample using the ideal gas law, we can divide the mass by the volume to find the density.
Since the units of density are typically g/L, we need to convert the units of volume from L to cm³, and divide the mass in grams by the volume in cm³ to find the density in g/cm³.
Using the given temperature of 70.0 °C, we convert it to Kelvin by adding 273.15 (343.15 K), and using the given pressure of 2.50 atm, we convert it to kPa by multiplying by 101.325 (253.3125 kPa).
We can then plug the values into the ideal gas law equation to calculate the volume of the sample. Next, we convert the volume from L to cm³, and divide the molar mass of water by the volume to find the density in g/cm³.
The correct answer would be A. 0.5 g/L.