Question

The pressure, P, of a gas varies directly with its temperature, T, and inversely with its volume, V, according to the equation formula to find pressure, where n is the number of molar units and R is the universal gas constant. One molar unit of a gas has a pressure of about 1,245 joules at a temperature of 300 Kelvin and a volume of 2 liters. What is the pressure of the same number of molar units of the gas at a temperature of 400 Kelvin and a volume of 2.5 liters?

a)1,328 joules
b)1,900 joules
c)2,375 joules
d)2,600 joules

Answer 1

As we know by ideal gas equation that

PV = nRT

here

n = number of moles

R = universal gas constant

T = temperature

P = pressure

V = volume

now here we have two set of data for same number of moles

so we will have

`(P_1V_1)/(RT_1)= (P_2V_2)/(RT_2)`

now we have

`(1245* 2)/(R(300)) = (P_2(2.5))/(R(400))`

now we have to solve it for pressure

`P_2 = (1245* 2 * 400)/(300* 2.5)`

`P_2 = 1328 joules`

Answer 2

The equation formula:
P V = n R T
1,245 * 2 l = n R * 300 K
n R = 1,245 * 2 : 300 = 8.3
P * 2.5 l = n R * 400 K
P * 2.5 = 8.3 * 400
P = 3,320 : 2.5 = 1328 J
Answer: A ) 1,328 joules.