The van der Waals equation of state was designed (by Dutch physicist Johannes va
ID: 578147 • Letter: T
Question
The van der Waals equation of state was designed (by Dutch physicist Johannes van der Waals) to predict the relationship between pressure p, volume V and temperature Tfor gases better than the Ideal Gas Law does p+ a-| (V_ n b)= n RT The van der waals equation of state. R stands for the gas constant and n for moles of gas. The parameters a and b must be determined for each gas from experimental data Use the van der Waals equation to answer the questions in the table below What are the units of a? mol What are the units of b? mol For carbon dioxide the numerical value of a is 3.592 and the numerical value of b is 0.0429 atm Use the van der Waals equation to calculate the pressure of a sample of carbon dioxide at 100.0 °C with a molar volume of 3.47 L/mol. Round your answer to 3 significant digits Use the Ideal Gas Law to calculate the pressure of the same sample under the same conditions. Round this answer to 3 significant digits also atmExplanation / Answer
1)
unit of p + an^2/v^2 should be atom
So,
unit of an^2/v^2 should be atom
so, unit of a = atm/L^2/mol^2
2)
unit of V-nb should be L
so,
unit of nb should be L
so,
unit of b = L/mol
3)
Given:
V = 3.47 L
n = 1.0 mol
R = 0.0821 atm.L/mol.K
T = 373.0 K
a = 3.592 atm.L^2/mol^2
b = 0.0429 L/mol
use:
(P+an^2/V^2)*(V-nb) = n*R*T
(P + 3.592*1.0^2/3.47^2)*(3.47-1.0*0.0429) = 1.0*0.0821*373.0
(P + 0.2983)*(3.4271) = 30.6233
P + 0.2983 = 8.9356
P = 8.64 atm
Answer:
4)
Given:
V = 3.47 L
n = 1 mol
T = 100.0 oC
= (100.0+273) K
= 373 K
use:
P * V = n*R*T
P * 3.47 L = 1 mol* 0.08206 atm.L/mol.K * 373 K
P = 8.8209 atm
Answer: 8.82 atm
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