Final answer:
To find the volume of 2.40 moles of gas at 50.0°C and 2.00 atm, we use the ideal gas law. After converting the temperature to Kelvin, we calculate the volume using the formula V = nRT/P and determine the volume to be 31.74 liters.
Step-by-step explanation:
The question asks to find the volume of a gas given the amount in moles, pressure, and temperature. To determine the volume of 2.40 moles of gas at a pressure of 2.00 atm and a temperature of 50.0°C, we use the ideal gas law, which is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T is temperature in Kelvin. The first step is to convert the temperature from Celsius to Kelvin by adding 273.15, which gives us 323.15 K.
We proceed by rearranging the ideal gas law to solve for volume (V):
V = nRT/P. Substituting in the known values, we get: V = (2.40 moles) * (0.0821 L·atm/(K·mol)) * (323.15 K) / (2.00 atm). Calculating this, we find the volume of the gas to be:
V = 2.40 * 0.0821 * 323.15 / 2.00 = 31.74 L. Therefore, the volume of the 2.40 moles of gas is 31.74 liters.