We are given a sample of gas and we know the initial temperature and pressure. The original volume is our unknown.
P₁ = 99.6 atm T₁ = 273.9 K V₁ = ?
We are told that the gas at the end of the process is at STP (standard temperature and pressure). The standard pressure is 1 atm and the standard temperature is 273.15 K. We are also given the final volume.
P₂ = 1 atm T₂ = 273.15 K V₂ = 429.1 mL
Since the temperature is not constant, we can use this formula to solve our problem:
P₁ * V₁ / T₁ = P₂ * V₂ / T₂
We can replace the given values and solve the equation for V1 to get the answer to our problem.
P₁ * V₁ / T₁ = P₂ * V₂ / T₂
V₁ = P₂ * V₂ * T₁/ (T₂ * P₁)
V₁ = 1 atm * 429.1 mL * 273.9 K/(273.15 K * 99.6 atm)
V₁ = 4.32 mL
Answer: the original volume of the gas was 4.32 mL.