How to Calculate the New Volume of Helium Gas at Increased Temperature and Pressure

What will be the new volume of the helium gas when the temperature is increased to 425.0K and the pressure is increased to 3.50 atm?

Given a sample of helium with a volume of 3.20x10² mL at STP, how can we calculate the new volume as the temperature and pressure increase?

Answer:

The new volume of the sample of helium gas as its temperature and pressure increases to the given values is 1.40×10² mL.

The Combined gas law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law to calculate the behavior of gases under changing conditions. It states that the ratio of the product of volume and pressure to the absolute temperature of a gas is constant.

The formula for the Combined gas law is: P₁V₁/T₁ = P₂V₂/T₂

Given the initial volume of helium gas V₁ = 3.20 × 10² mL = 0.32 L and initial pressure P₁ = 1.0 atm at standard temperature and pressure (T₁ = 273.15 K).

With final pressure P₂ = 3.50 atm and final temperature T₂ = 425.0 K, we need to calculate the final volume V₂.

Using the formula, we find: V₂ = (1.0 atm × 0.32 L × 425.0 K) / (3.50 atm × 273.15 K) = 1.40×10² mL.

Therefore, the new volume of the sample of helium gas as its temperature and pressure increase to the given values is 1.40×10² mL.