At 125 degrees Celsius, the pressure of a sample of He gas is 345 mmHg. At what temperature degrees Celsius will the pressure become 690 mm Hg, if the volume remains constant?
Since V is constant, if the pressure doubles, so does the temperature. Algebraically,
PV=kT
125°C = 398°K
(345)V = k(398)
(690)V = kT
T/398 = 690/345
T = 796°K = 523°C
To solve this problem, we can use the combined gas law equation, which states:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures of the gas,
V1 and V2 are the initial and final volumes of the gas, and
T1 and T2 are the initial and final temperatures of the gas.
In this case, the volume remains constant, so the equation simplifies to:
P1 / T1 = P2 / T2
Given that:
P1 = 345 mmHg (initial pressure)
T1 = 125 degrees Celsius (initial temperature)
P2 = 690 mmHg (final pressure)
Let's substitute these values into the equation to solve for T2:
345 mmHg / 125°C = 690 mmHg / T2
Now, we can cross-multiply:
(345 mmHg) * (T2) = (690 mmHg) * (125°C)
Divide both sides of the equation by 345 mmHg to solve for T2:
T2 = (690 mmHg * 125°C) / 345 mmHg
Simplifying further:
T2 ≈ 250°C
Therefore, the temperature at which the pressure becomes 690 mmHg, with a constant volume, is approximately 250 degrees Celsius.
To solve this problem, you can use the combined gas law equation which relates the pressure, temperature, and volume of a gas. The equation is:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures respectively,
V₁ and V₂ are the initial and final volumes respectively, and
T₁ and T₂ are the initial and final temperatures respectively.
In this problem, the volume remains constant, so we can simplify the equation to:
P₁ / T₁ = P₂ / T₂
Now let's plug in the given values. At 125 degrees Celsius, the pressure (P₁) is 345 mmHg. We need to find the temperature (T₂) when the pressure (P₂) becomes 690 mmHg.
345 / 125 = 690 / T₂
To find T₂, we can cross-multiply and then solve for T₂:
345 × T₂ = 690 × 125
Divide both sides by 345:
T₂ = (690 × 125) / 345
Now, calculate the value of T₂:
T₂ = 250 degrees Celsius
Therefore, at 250 degrees Celsius, the pressure of the sample of He gas will be 690 mmHg, assuming the volume remains constant.