Question

6dm³ of a dry gas is heated at temperature of 273°C has pressure of 380mm of Hg . Find the volume of gas at STP​

Answer 1

Given:

✰ Volume of dry gas ( V₁ ) = 6 dm³

✰ Temperature ( T₁ ) = 546 K

✰ Temperature ( T₂ ) = 273 K

✰ Pressure ( P₁ ) = 380 mm of Hg

✰ Pressure ( P₂ ) = 760 mm of Hg

To find:

✠ The volume of gas at STP ( V₂ ).

Solution:

Before going to the question, let's understand the concept!

Here, we will use gas equation to find the volume of gas at STP.

The equation is used for calculating changes in gas volume when both its pressure and temperature change.

Since volume of a gas changes remarkably with change in temperature and pressure. It becomes necessary to choose standard values of temperature and pressure to which the gas volume can be referred.

❖ The standard values of temperature is 273 K, while the standard value of pressure is 760 mm of Hg. These standard values are known as standard temperature and pressure.

Let's solve it...✧

Converting the given temperature T₂ in kelvin, we get T₁,

⟹ K = °C + 273

⟹ K = 273 + 273

⟹ K = 546 K

∴ The initial temperature of the given gas ( T₁ ) = 546 K

Applying the gas equation,

✭ (P₁V₁)/T₁ = (P₂V₂)/T₂✭

Here,

• P₁, V₁ and T₁ are initial pressure, volume and temperature respectively.
• P₂, V₂ and T₂ are final pressure, volume and temperature respectively.

Substituting the values in the equation, we have:

➤ ( 380 × 6 )/546 = ( 760 × V₂ )/273

➤ V₂ = ( 380 × 6 × 273 )/( 546 × 760 )

➤ V₂ = ( 1 × 6 × 1 )/( 2 × 2 )

➤ V₂ = ( 1 × 3 × 1 )/( 1 × 2 )

➤ V₂ = 3/2

➤ V₂ = 1.5 dm³

∴ The volume of gas at STP ( V₂ ) = 1.5 dm³

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