PHYSICS HIGH SCHOOL

Assume that you have 0.480 mol of N2 in a volume of 0.700 L at 300 K . 1. Calculate the pressure in atmospheres using the ideal gas law.
2. Calculate the pressure in atmospheres using the van der Waals equation. For N2 , a=1.35 (L2⋅atm)/mol2 , and b=0.0387 L/mol

Answers

Answer 1
Answer:

Answer:

1) 16.88 atm

2) 34.47 atm

Explanation:

Data:

Volume=0.700L

Temperature = 300K

Number of moles=0.480 mol

Ideal gas constant=0.082057 L*atm/K·mol

1) The ideal gas law is:

PV=nRT (1)

with P the pressure, T the temperature, n the number of moles, V the volume and R the ideal gas constant , so solvig (1) for P:

P=(nRT)/(V)

P=((0.480)(0.082057)(300))/(0.700)=16.88 atm

2) The vander Walls equation is:

(P+(a)/(V^(2)))(V-b)=RT

solving for P

P=(RT)/(V-b)-(a)/(V^2)=((0.082057)(300))/(0.700-0.0387)-(1.35)/(0.700^2)=34.47 atm
Answer 2
Answer:

The pressure in atmospheres is 0.974 atm using the ideal gas law and 0.962 atm using the van der Waals equation for N2.

1. To calculate the pressure in atmosphere using the ideal gas law, we can use the equation 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/mol·K), and T is the temperature in Kelvin.

Rearranging the equation, we have P = (nRT)/V. Plugging in the given values, we get P = (0.480 mol * 0.0821 L·atm/mol·K * 300 K) / 0.700 L = 0.974 atm.

2. To calculate the pressure in atmosphere using the van der Waals equation, we can use the equation (P + an^2/V^2)(V - nb) = nRT, where a and b are constants specific to the gas being used. Rearranging the equation, we have P = (nRT/(V - nb)) - an^2/V^2.

Plugging in the given values and the constants for N2, we get P = (0.480 mol * 0.0821 L·atm/mol·K * 300 K/(0.700 L - 0.0387 L/mol * 0.480 mol))^2 - 1.35 (L^2·atm)/mol^2 * (0.480 mol)^2/(0.700 L)^2 = 0.962 atm.

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