If a gas is cooled from 323.0 K to 273.15 K and the volume is kept constant, what final pressure would result if the original pressure was 750.0 mm Hg? Round to the nearest tenth. Don't forget the units.
To calculate the final pressure of the gas when it is cooled from 323.0 K to 273.15 K, while keeping the volume constant, you can use the ideal gas law equation:
P1/T1 = P2/T2
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Given:
P1 = 750.0 mm Hg
T1 = 323.0 K
T2 = 273.15 K
Plugging in these values into the equation, we have:
750.0 mm Hg / 323.0 K = P2 / 273.15 K
Cross-multiplying, we get:
P2 = (750.0 mm Hg * 273.15 K) / 323.0 K
Calculating this expression, we find:
P2 ≈ 634.4 mm Hg
So, the final pressure of the gas, when cooled from 323.0 K to 273.15 K with constant volume, would be approximately 634.4 mm Hg.
To find the final pressure when a gas is cooled from one temperature to another and the volume is kept constant, we can use Charles's Law, which states that the volume of a given amount of gas is directly proportional to its absolute temperature. In this case, since the volume is constant, we can assume the pressure and temperature are directly proportional as well.
We can express Charles's Law mathematically as:
(P₁/T₁) = (P₂/T₂)
where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.
Let's plug in the given values into the equation:
P₁ = 750.0 mm Hg
T₁ = 323.0 K
T₂ = 273.15 K
(P₁/T₁) = (P₂/T₂)
Now, we can solve for P₂ by rearranging the equation:
P₂ = (P₁ * T₂) / T₁
Now, let's substitute the values:
P₂ = (750.0 mm Hg * 273.15 K) / 323.0 K
Calculating this expression gives us:
P₂ ≈ 633.7 mm Hg
Therefore, the final pressure, when a gas is cooled from 323.0 K to 273.15 K, with the volume kept constant, would be approximately 633.7 mm Hg.