Final answer:
To calculate the pressure exerted by 1.00 mol of CO2 in a 1.00 L vessel at 300 K, we can use the ideal gas equation: PV = nRT. The pressure is 24.63 atm. To calculate the pressure using the van der Waals equation, we need to consider the volume correction factor (b) and the attraction correction factor (a). The pressure is 23.50 atm.
Step-by-step explanation:
To calculate the pressure exerted by 1.00 mol of CO2 in a 1.00 L vessel at 300 K, we can use the ideal gas equation: PV = nRT. In this case, we know the volume (V = 1.00 L), the number of moles (n = 1.00 mol), and the temperature (T = 300 K). To find the pressure (P), we can rearrange the equation to P = (nRT) / V. Substituting the values, we get P = (1.00 mol)(0.0821 L·atm/mol·K)(300 K) / (1.00 L) = 24.63 atm.
For part 2, to calculate the pressure using the van der Waals equation, we need to consider the volume correction factor (b) and the attraction correction factor (a). The van der Waals equation is (P + (an^2 / V^2))(V - nb) = nRT, where a and b are constants specific to the gas. For CO2, a = 3.59 atm·L^2/mol^2 and b = 0.0427 L/mol. Rearranging the equation to solve for P, we get P = (nRT) / (V - nb) - (an^2 / V^2). Substituting the values, we get P = (1.00 mol)(0.0821 L·atm/mol·K)(300 K) / (1.00 L - (0.0427 L/mol)(1.00 mol)) - (3.59 atm·L^2/mol^2)(1.00 mol^2) / (1.00 L^2) = 23.50 atm.