A sample of nitrogen gas at a pressure of 786 mm Hg and a temperature of 57 °C, occupies a volume of 10.5 liters. If the gas is heated at constant pressure to a temperature of 97 °C, the volume of the gas sample will be____
Use (V1/T1) = (V2/T2).
Remember to convert degrees C to degrees K.
K = C + 273
post your work if you get stuck.
To find the volume of the gas sample when it is heated from 57 °C to 97 °C at constant pressure, you can use the combined gas law formula:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure (same as initial pressure in this case)
V₂ = final volume (to be determined)
T₂ = final temperature
Given:
P₁ = 786 mm Hg
V₁ = 10.5 liters
T₁ = 57 °C
P₂ = 786 mm Hg (constant pressure)
T₂ = 97 °C
Now, substitute the values into the formula:
(786 mm Hg * 10.5 liters) / (57 °C) = (786 mm Hg * V₂) / (97 °C)
Simplifying:
786 mm Hg * 10.5 liters / 57 °C = 786 mm Hg * V₂ / 97 °C
Multiply both sides by 97 °C:
(786 mm Hg * 10.5 liters / 57 °C) * 97 °C = 786 mm Hg * V₂
Canceling out the units:
(786 * 10.5) liters = V₂
Solving for V₂:
V₂ = 8201.5 liters
Therefore, the volume of the gas sample will be 8201.5 liters when the gas is heated at constant pressure to a temperature of 97 °C.
To solve this problem, we can use the combined gas law formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes, and
T1 and T2 are the initial and final temperatures.
Given:
P1 = 786 mm Hg (initial pressure)
T1 = 57 °C (initial temperature)
V1 = 10.5 liters (initial volume)
T2 = 97 °C (final temperature)
We need to find V2, the final volume.
Now, let's substitute the given values into the formula and solve for V2:
(786 mm Hg * 10.5 L) / (57 °C) = (P2 * V2) / (97 °C)
To solve for V2, we can cross-multiply and divide:
(786 mm Hg * 10.5 L * 97 °C) / (57 °C) = P2 * V2
V2 = (786 mm Hg * 10.5 L * 97 °C) / (57 °C * P2)
Since the problem states that the gas is heated at constant pressure, we can assume the final pressure P2 remains the same as the initial pressure P1.
Therefore, we can substitute P2 = P1 = 786 mm Hg:
V2 = (786 mm Hg * 10.5 L * 97 °C) / (57 °C * 786 mm Hg)
The term "786 mm Hg" cancels out, and we get:
V2 = (10.5 L * 97 °C) / (57 °C)
V2 ≈ 17.89 liters
Therefore, the volume of the gas sample at a temperature of 97 °C will be approximately 17.89 liters.