a balloon is filled with 15 L of an ideal gas of 20C. at this temperature the pressure of the gas is 1520 mm Hg. Suppose that the volume of the gas is reduced to 5 L at 290 K. what is the new pressure of the gas in atmospheres?
Use (P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To solve this problem, we can use the combined gas law formula:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ = Initial pressure of the gas (1520 mm Hg)
V₁ = Initial volume of the gas (15 L)
T₁ = Initial temperature of the gas in Kelvin (20 + 273 = 293 K)
P₂ = Final pressure of the gas (what we want to find)
V₂ = Final volume of the gas (5 L)
T₂ = Final temperature of the gas in Kelvin (290 K)
Now let's substitute the values into the formula and solve for P₂:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
(P₂ * V₂) = (P₁ * V₁ * T₂) / T₁
P₂ = (P₁ * V₁ * T₂) / (V₂ * T₁)
P₂ = (1520 * 15 * 290) / (5 * 293)
P₂ = 6455200 / 1465
P₂ ≈ 4410.85 mm Hg
To convert this pressure from mm Hg to atmospheres, we can use the conversion factor:
1 atmosphere = 760 mm Hg
P₂ ≈ 4410.85 / 760
P₂ ≈ 5.8 atmospheres
Therefore, the new pressure of the gas is approximately 5.8 atmospheres.