A gas has a volume of 50.0 cm3 at a temperature of -73°C. What volume would the gas occupy at a temperature of -123°C if the pressure stays constant?
(V1/T1) = (V2/T2)
T must be in kelvin.
37.5 cm3
To solve this problem, we can use the ideal gas law formula which states that PV = nRT, where:
P is the pressure,
V is the volume,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature in Kelvin.
First, let's convert the given temperatures from Celsius to Kelvin:
-73°C + 273.15 = 200.15 K
-123°C + 273.15 = 150.15 K
Since the pressure is constant, we can simplify the equation to:
V1/T1 = V2/T2
Now, substitute the given values:
V1 = 50.0 cm^3
T1 = 200.15 K
T2 = 150.15 K
Rearrange the equation to solve for V2:
V2 = (V1 * T2) / T1
Calculate the value:
V2 = (50.0 cm^3 * 150.15 K) / 200.15 K
V2 ≈ 37.5 cm^3
Therefore, the gas would occupy a volume of approximately 37.5 cm^3 at a temperature of -123°C, assuming the pressure remains constant.
To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, volume, and temperature of a gas to the final pressure, volume, and temperature of the gas is constant, as long as the pressure remains constant.
The combined gas law formula is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Let's plug in the given values:
P1 = unknown (we know the pressure stays constant, so it is not needed in this calculation)
V1 = 50.0 cm3
T1 = -73°C
T2 = -123°C
Using the equation, we can rearrange it to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Since the pressure remains constant, we can eliminate it from the equation:
V2 = (V1 * T2) / T1
Now, let's substitute the values and calculate V2:
V2 = (50.0 cm3 * -123°C) / -73°C
Here, the unit of °C cancels out, leaving us with:
V2 = (50.0 cm3 * -123) / -73
Simplifying the expression:
V2 ≈ -83.561 cm3
Therefore, the gas would occupy a volume of approximately -83.561 cm3 at a temperature of -123°C, with constant pressure.