Final answer:
The ratio of the density of water to the density of air, pw/pa, can be calculated using the ideal gas law. Use the given pressure, temperature, and molar masses to calculate the densities of water and air, and then find the desired ratio.
Step-by-step explanation:
The ratio of the density of water to the density of air, pw/pa, can be calculated using the ideal gas law. The ideal gas law states that 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. By rearranging the equation, we can solve for density (p) as p = (PM)/(RT), where P is the pressure, M is the molar mass, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, the pressure is 5 atmospheres, which can be converted to Pascals (1 atmosphere = 101,325 Pascals). The molar mass of water is 18 g/mol, and the molar mass of air (approximately) is 28.97 g/mol. The ideal gas constant is 8.314 J/(mol·K). The temperature is given as 100°C, which is 373.15 Kelvin. Substituting these values into the equation, we can calculate the density of water and air.
After calculating the densities, the ratio of the density of water to the density of air can be calculated as pw/pa.