A sample of helium gas has a pressure of 860 mm Hg at a temperature of 225 K. At what pressure (mm Hg) will the helium sample reach a temperature of 675 K.
At constant volume, P/T = constant.
P1/T1 = 860/225 = P2/T2 = P2/675
P2 = 2580 mm Hg will be the final pressure.
It must triple because the absolute temperature triples.
To solve this problem, we can use the ideal gas law, which states that the pressure (P) of a gas is directly proportional to its temperature (T) in Kelvin, given a constant volume (V) and a constant number of moles (n). The relationship is expressed as:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas in Kelvin
In this problem, we are only interested in the pressure and temperature relationship. Thus, we can rearrange the ideal gas law equation to solve for pressure:
P = (nRT) / V
Since the number of moles, volume, and gas constant are all constant, we can write the equation as:
P₁ / T₁ = P₂ / T₂
Where:
P₁ = initial pressure
T₁ = initial temperature
P₂ = final pressure (what we want to find)
T₂ = final temperature
Let's plug in the values given in the problem to find the final pressure:
P₁ = 860 mm Hg
T₁ = 225 K
T₂ = 675 K
P₂ / 225 K = 860 mm Hg / 675 K
Now we can solve for P₂ by cross-multiplying and isolating P₂:
P₂ = (860 mm Hg / 675 K) * 225 K
P₂ ≈ 287.41 mm Hg
Therefore, the helium sample will reach a pressure of approximately 287.41 mm Hg when the temperature is 675 K.