A sample of neon gas has an initial volume of 2.5L at 300 K. What is the new temperature of the gas(both in K and Celsius degrees) if the pressure remains constant, when the volume is changed to each of the following values: a. 5.00L b. 7.50L c. 1.50L d. 500mL e. 50.0mL f. 750mL
Assuming ideal gas, we can use Charles Law:
V1 / T1 = V2 / T2
where
V = volume
T = absolute temperature (K)
It's just direct substitution. I'll do (a):
V1 / T1 = V2 / T2
2.5 / 300 = 5 / T2
Solve for the new temperature (T2):
2.5(T2) = 300(5)
T2 = 1500 / 2.5
T2 = 600 K
Now try doing the others. Hope this helps~ `u`
To find the new temperature of the gas, we can use the combined gas law equation, which states that the initial pressure multiplied by the initial volume divided by the initial temperature is equal to the final pressure multiplied by the final volume divided by the final temperature.
Given:
Initial volume (V1) = 2.5 L
Initial temperature (T1) = 300 K
a. New volume (V2) = 5.00 L
Using the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
We assume the pressure (P1) remains constant, so we can write:
(V1) / T1 = (V2) / T2
Plugging in the values:
(2.5) / 300 = (5.00) / T2
Solving for T2:
T2 = (5.00) / [(2.5) / 300]
T2 = 600 K
To convert to Celsius degrees:
Celsius = K - 273.15
Celsius = 600 - 273.15
Celsius = 326.85 °C
b. New volume (V2) = 7.50 L
Using the same equation:
T2 = (7.50) / [(2.5) / 300]
T2 = 900 K
Celsius = 900 - 273.15
Celsius = 626.85 °C
c. New volume (V2) = 1.50 L
T2 = (1.50) / [(2.5) / 300]
T2 = 180 K
Celsius = 180 - 273.15
Celsius = -93.15 °C
d. New volume (V2) = 500 mL = 0.5 L
T2 = (0.5) / [(2.5) / 300]
T2 = 60 K
Celsius = 60 - 273.15
Celsius = -213.15 °C
e. New volume (V2) = 50.0 mL = 0.05 L
T2 = (0.05) / [(2.5) / 300]
T2 = 6 K
Celsius = 6 - 273.15
Celsius = -267.15 °C
f. New volume (V2) = 750 mL = 0.75 L
T2 = (0.75) / [(2.5) / 300]
T2 = 90 K
Celsius = 90 - 273.15
Celsius = -183.15 °C
So, the new temperatures in Kelvin for each volume are:
a. 600 K
b. 900 K
c. 180 K
d. 60 K
e. 6 K
f. 90 K
And the corresponding temperatures in Celsius degrees are:
a. 326.85 °C
b. 626.85 °C
c. -93.15 °C
d. -213.15 °C
e. -267.15 °C
f. -183.15 °C
To find the new temperature of the gas when the volume changes, we can use the combined gas law equation:
(P1 x V1) / T1 = (P2 x V2) / T2
where:
P1 is the initial pressure of the gas (which remains constant in this case)
V1 is the initial volume of the gas
T1 is the initial temperature of the gas
P2 is the pressure of the gas (which remains constant in this case)
V2 is the new volume of the gas
T2 is the new temperature of the gas
We can rearrange the equation to solve for T2:
T2 = (P2 x V2 x T1) / (P1 x V1)
Given:
P1 = P2 (constant pressure)
V1 = 2.5L (initial volume)
T1 = 300K (initial temperature)
Let's calculate the new temperatures for each given volume:
a. V2 = 5.00L
T2 = (P2 x V2 x T1) / (P1 x V1)
T2 = (P2 x 5.00L x 300K) / (P1 x 2.5L)
b. V2 = 7.50L
T2 = (P2 x V2 x T1) / (P1 x V1)
T2 = (P2 x 7.50L x 300K) / (P1 x 2.5L)
c. V2 = 1.50L
T2 = (P2 x V2 x T1) / (P1 x V1)
T2 = (P2 x 1.50L x 300K) / (P1 x 2.5L)
d. V2 = 500mL = 0.500L
T2 = (P2 x V2 x T1) / (P1 x V1)
T2 = (P2 x 0.500L x 300K) / (P1 x 2.5L)
e. V2 = 50.0mL = 0.0500L
T2 = (P2 x V2 x T1) / (P1 x V1)
T2 = (P2 x 0.0500L x 300K) / (P1 x 2.5L)
f. V2 = 750mL = 0.750L
T2 = (P2 x V2 x T1) / (P1 x V1)
T2 = (P2 x 0.750L x 300K) / (P1 x 2.5L)
To calculate the temperatures in Celsius, you can simply convert the Kelvin temperatures to Celsius by subtracting 273.15 from each value.