Question

The temperature of 2.5 L of a gas initially at STP is raised to 250°C at constant volume. Calculate the final pressure of

the gas in atm.

Answer 1

To calculate the final pressure of the gas, we can use the combined gas law, which states:

(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂

Where:

P₁ = Initial pressure of the gas

V₁ = Initial volume of the gas

T₁ = Initial temperature of the gas

P₂ = Final pressure of the gas (what we're trying to find)

V₂ = Final volume of the gas (since the volume is constant, V₂ = V₁)

T₂ = Final temperature of the gas

Given:

V₁ = 2.5 L

T₁ = Standard Temperature and Pressure (STP) = 273.15 K

T₂ = 250°C = 250 + 273.15 = 523.15 K

We can rearrange the formula and solve for P₂:

(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂

Since V₂ = V₁ (constant volume):

P₁ / T₁ = P₂ / T₂

Plugging in the values:

P₁ / 273.15 K = P₂ / 523.15 K

Now, let's assume that the initial pressure is at standard pressure (STP), which is 1 atmosphere (atm):

1 atm / 273.15 K = P₂ / 523.15 K

To find P₂, we can cross-multiply and solve for it:

P₂ = (1 atm) × (523.15 K) / (273.15 K)

P₂ ≈ 1.91 atm

Therefore, the final pressure of the gas at a temperature of 250°C and constant volume is approximately 1.91 atm.

Step-by-step explanation: