A sample of helium gas occupies a 10 cubic meter container at STP (273 K, 1 atm). What will the approximate volume become when the pressure is 1.5 atm and the temperature is 32 oC?
(P1V1/T1) = (P2V2/T2)
I believe the answer would be 7.4 cubic meters
To solve this problem, we can use the combined gas law equation, which relates the pressure, volume, and temperature of a gas. The equation is given as:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ and P₂ are the initial and final pressures
V₁ and V₂ are the initial and final volumes
T₁ and T₂ are the initial and final temperatures
First, we need to convert the initial and final temperatures to Kelvin. To convert Celsius to Kelvin, we add 273 to the Celsius temperature. So, the initial temperature T₁ is 273 K and the final temperature T₂ is (32 + 273) K = 305 K.
Now, let's plug the given values into the equation:
(1 atm * 10 m³) / (273 K) = (1.5 atm * V₂) / (305 K)
Simplifying this equation, we get:
10 m³ / 273 K = (1.5 atm * V₂) / 305 K
To solve for V₂, we can cross-multiply and then divide:
10 m³ / 273 K * 305 K = 1.5 atm * V₂
V₂ = (10 m³ / 273 K * 305 K) / (1.5 atm)
Calculating this, we find:
V₂ ≈ 11.4 m³
Therefore, the approximate volume will become around 11.4 cubic meters when the pressure is 1.5 atm and the temperature is 32 °C.