Gas Law Calculation: Finding the Volume of an Ideal Gas
How can we calculate the volume of an ideal gas when the temperature and pressure change?
Given a sample of an ideal gas with an initial volume of 3.50 L at 14.40 °C and 1.60 atm, what is the volume of the gas at 21.20 °C and 0.990 atm?
Calculation and Solution:
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature of an ideal gas. The combined gas law formula is:
(P1 × V1) / T1 = (P2 × V2) / T2
Given:
P1 = 1.60 atm
V1 = 3.50 L
T1 = 14.40 °C + 273.15 = 287.55 K
P2 = 0.990 atm
T2 = 21.20 °C + 273.15 = 294.35 K
Using the formula and substituting the given values, we can solve for V2:
(1.60 atm × 3.50 L) / 287.55 K = (0.990 atm × V2) / 294.35 K
Cross-multiplying and solving for V2 gives:
V2 = (1.60 atm × 3.50 L × 294.35 K) / (0.990 atm × 287.55 K)
V2 ≈ 6.01 L