an ideal gas in a closed inflexible container has a pressure of 6 atms and a temperature of 27 degree c. What will be the new pressure of gas of temperature is decreased to -73 degree c.
1) 2atm
2) 3atm
3) 4atm
4) 8atm
5) 9atm
5)9atm
I don't believe 5)9 atm is correct.
Use (P1/T1) + (P2/T2). Don't forget to convert T to Kelvin.
2 atm
To solve this problem, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the initial temperature and the final temperature to Kelvin. To convert Celsius to Kelvin, we add 273.15:
Initial temperature (in Kelvin) = 27°C + 273.15 = 300.15 K
Final temperature (in Kelvin) = -73°C + 273.15 = 200.15 K
Now, let's use the ideal gas law equation to find the initial number of moles of gas (n1):
P1V = n1RT1
Since the volume (V) and the number of moles (n) are constant, we can rewrite the equation as:
P1/T1 = n1R
Now, we can rearrange the equation to solve for n1:
n1 = (P1 * T1) / R
Substituting the given values:
n1 = (6 atm * 300.15 K) / (0.0821 L·atm/(mol·K))
n1 ≈ 218.93 mol
Next, let's find the final pressure (P2) when the temperature decreases to -73°C. Here, the number of moles (n) remains the same, and we can use the ideal gas law equation again:
P2V = nRT2
Since the volume (V) and the number of moles (n) are constant, we can rewrite the equation as:
P2/T2 = nR
Now, we can rearrange the equation to solve for P2:
P2 = (n * R * T2) / V
Since the volume (V) is constant and not provided, we can assume it remains constant in this problem. Therefore, the volume cancellation allows us to drop the "V" from the equation:
P2 = n * R * T2
Substituting the values:
P2 = 218.93 mol * 0.0821 L·atm/(mol·K) * 200.15 K
P2 ≈ 3603.45 atm
However, we are asked for the pressure in atmospheres, not in thousands of atmospheres. So, we need to divide the result by 1000:
P2 ≈ 3.60 atm
Therefore, the new pressure of the gas, when the temperature is decreased to -73°C, would be approximately 3.60 atm.
So, the correct answer from the given options would be:
2) 3atm