When solid carbon dioxide (dry ice) vaporizes to gas, it undergoes a phase change from solid to gas without melting into a liquid. This process is called sublimation.
To calculate the volume of gas produced, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to determine the number of moles of gas produced. We can use the molar mass of carbon dioxide to convert from mass to moles:
moles of CO2 = mass of dry ice / molar mass of CO2
moles of CO2 = 500.0 g / 44.0 g/mol
moles of CO2 = 11.36 mol
Since the dry ice sublimes directly to a gas, all of the moles of CO2 will be in the gas phase.
Next, we can plug in the values we know into the ideal gas law:
PV = nRT
V = nRT / P
where R is the ideal gas constant, which has a value of 0.08206 L·atm/(mol·K).
Converting the temperature to Kelvin:
T = 25.0 °C + 273.15 = 298.15 K
Plugging in the values:
V = (11.36 mol) x (0.08206 L·atm/(mol·K)) x (298.15 K) / (1.75 atm)
V = 439.4 L
Therefore, the volume of gas produced is approximately 439.4 L.