If a volume of nitric oxide gas at 25.0°C increases from 2.00 L to 3.00 L, what is the final Celsius temperature? Assume pressure remains constant
38 C
To find the final Celsius temperature, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant)
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the initial and final temperatures from Celsius to Kelvin:
Initial temperature = 25.0°C + 273.15 K = 298.15 K
Final temperature = ? K (unknown)
Next, using the ideal gas law equation, we can set up a ratio between the initial and final conditions:
(P * V) / T_initial = (P * V) / T_final
Since the pressure (P) remains constant,
(V / T_initial) = (V / T_final)
Simplifying the ratio, we get:
1 / T_initial = 1 / T_final
Now, let's substitute the values into the equation:
1 / 298.15 K = 1 / T_final
To find T_final, we can simply take the reciprocal of both sides:
T_final = 1 / (1 / 298.15) K
Simplifying further:
T_final = 298.15 K
Therefore, the final Celsius temperature is 25.0°C.
To find the final Celsius temperature, we can use the ideal gas law equation, which states:
PV = nRT
where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
Since the question states that the pressure remains constant, we can consider it to be constant and cancel it out from the equation. Therefore, the equation becomes:
V/T = nR/P
We can rewrite the equation to solve for the final temperature:
T = (V2/V1) * T1
where:
T1 is the initial temperature in Kelvin
V1 is the initial volume of the gas
V2 is the final volume of the gas
First, we need to convert the initial temperature from Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.
Given:
Initial temperature (T1) = 25.0°C = 25.0 + 273.15 = 298.15 K
Initial volume (V1) = 2.00 L
Final volume (V2) = 3.00 L
Now we can substitute the values into the equation to find the final temperature:
T = (V2 / V1) * T1
T = (3.00 L / 2.00 L) * 298.15 K
T = 1.5 * 298.15 K
T ≈ 447.23 K
Finally, we convert the temperature back to Celsius by subtracting 273.15:
Final temperature = 447.23 K - 273.15 ≈ 174.08°C
Therefore, the final Celsius temperature is approximately 174.08°C.