Question

If 0.2 moles of hydrogen gas occupies an inflexible container with a capacity of 45 ml. and the temperature is raised from 25 C to 30 C, what is the change in pressure of the contained gas, assuming ideal behavior?

Answer 1

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Answer 2

Given: Moles of Hydrogen gas = 0.2

The capacity$\frac{P1(45)}{298} = \frac{P2(45)}{303}$ of the inflexible container = 45ml = 0.045 l (1l = 1000ml)

Initial temperature = 25°C

Final Temperature  = 30°C

To Find: Change in pressure

Solution:

Since the container is inflexible, the volume of the container will not change.

Let the initial pressure be P₁

Let the final pressure be P₂

Temperature in Kelvin = Temperature in Celsius + 273

Initial temperature in Kelvin(T₁) = 25 + 273

T₁ = 298 K

Final temperature in Kelvin(T₂) = 30 + 273

T₂ = 303K

According to the Ideal Gas Law

PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the Gas constant and T is the temperature

P x 0.045 = 0.2 x 0.083 x 298                       (R =0.083 L.bar.K⁻¹mol⁻¹ )

P = $\frac{49468}{450}$

P₁ = 109.92 bar

According to the Gas Law

$\frac{P1V1}{T1} = \frac{P2V2}{T2}$

$\frac{P1(45)}{298} = \frac{P2(45)}{303}$

P₂ = $\frac{303P1}{298}$

Change in pressure = Final pressure (P₂)  -  Initial Pressure(P₁)

                                  = $\frac{303P1}{298}$ - P1

                                  = $\frac{5P1}{298}$

                                  = $\frac{5(109.92)}{298}$

                                  = $\frac{549.6}{298}$

                                  = 1.84 bar

Therefore, the change in pressure is  1.84 bar