A sample of gas occupies 100ml at 27degree Celsius and 740mm pressure. The temperature the gas will have,when its volume is changed to 80ml at 740mm pressure is?

Question

A sample of gas occupies 100ml at 27degree Celsius and 740mm pressure. The temperature the gas will have,when its volume is changed to 80ml at 740mm pressure is?

Answer 1

To find the temperature of the gas when its volume is changed, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature

First, we need to determine the initial number of moles of gas. To do this, we can use the equation:

n = PV / (RT)

Given:
P₁ = 740 mmHg (pressure)
V₁ = 100 ml (volume)
T₁ = 27 °C (temperature)

We need to convert the temperature to Kelvin since the ideal gas law requires temperature in Kelvin.

T₁ = 27 °C + 273.15 = 300.15 K

Next, we can calculate the initial number of moles:

n₁ = (P₁ * V₁) / (R * T₁)

Assuming constant moles of gas, we can now find the final temperature when the volume is changed to 80 ml.

V₂ = 80 ml (new volume)
P₂ = 740 mmHg (pressure)

We need to find the new temperature T₂.

Using the ideal gas law again:

n₂ = (P₂ * V₂) / (R * T₂)

Since the number of moles (n) remains constant, we can equate n₁ and n₂:

(P₁ * V₁) / (R * T₁) = (P₂ * V₂) / (R * T₂)

Now, we can solve for T₂:

T₂ = (P₂ * V₂ * T₁) / (P₁ * V₁)

Plugging-in the given values:

T₂ = (740 mmHg * 80 ml * 300.15 K) / (740 mmHg * 100 ml)

Calculating this expression, we can find the temperature, T₂.

Answer 2

To find the temperature of the gas when its volume changes from 100 ml to 80 ml at constant pressure, we can use the combined gas law formula. The combined gas law equation is:

(P1 × V1) / T1 = (P2 × V2) / T2

Where:
P1 = initial pressure (in mmHg)
V1 = initial volume (in ml)
T1 = initial temperature (in Kelvin)
P2 = final pressure (in mmHg)
V2 = final volume (in ml)
T2 = final temperature (in Kelvin)

Given:
P1 = 740 mmHg
V1 = 100 ml
T1 = 27°C + 273.15 (to convert to Kelvin) = 300.15 K
P2 = 740 mmHg
V2 = 80 ml
T2 = ?

Substituting the given values into the combined gas law equation:

(740 × 100) / 300.15 = (740 × 80) / T2

Simplifying the equation:

74000 / 300.15 = 59200 / T2

Cross-multiplying:

74000 × T2 = 300.15 × 59200

Dividing both sides by 74000:

T2 ≈ (300.15 × 59200) / 74000

Calculating the result:

T2 ≈ 240.12 K

Therefore, the temperature of the gas will be approximately 240.12 Kelvin when its volume is changed to 80 ml at 740 mmHg pressure.