a container of 2.00 moles of an ideal gas as 1000 K undergoes a constant pressure and volume process in which the number of moles is increased to 5moles. what is the final temperature of the gas.
How do I start this? Do I somehow use the ideal gas law?
Use PV=nRT
so R=P1V1/n1T1
and R=P1V1/n2T2
R=P1V1/n1T1=P1V1/n2T2
n1T=n2T2
I got the answer to be 400. But can you explain to me those formulas? I'm still a bit confuse on how you got them. Where do these P1 and P2 and T1 and T2 come from
The original formula is
PV=nRT
for the question given we have a set of starting conditions
P=P1
V=V1
n=n1
T=T1
hence
P1 x V1=n1 x R x T1
which rearranges to
R=P1V1/n1T1
the second set of conditions is
P=P1
V=V1
(because P1 and V1 are constant in the question)
T=T2
N=n2
so
R=P1V1/n2T2
as R is the same in both cases
R=P1V1/n1T1=P1V1/n2T2
which rearranges to
n1T=n2T2
Yes, you can use the ideal gas law to solve this problem. The ideal gas law relates the pressure, volume, number of moles, and temperature of a gas. It can be expressed as:
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 of the gas in Kelvin
In this problem, you are given the initial conditions (2.00 moles of gas at 1000 K) and asked to find the final temperature when the number of moles is increased to 5 moles.
To solve the problem, follow these steps:
1. Convert the initial and final number of moles to moles (since the ideal gas law uses moles as its unit).
- Initial moles: 2.00 moles
- Final moles: 5 moles
2. Solve for the initial pressure using the ideal gas law equation:
PV = nRT
Rearrange the equation to solve for P:
P = (nRT) / V
Plug in the given values:
- Initial pressure: P1 = (2.00 mol * 8.314 J/(mol·K) * 1000 K) / V
3. Since the process is constant pressure and volume, the initial and final pressures are the same (P1 = P2). Therefore, you can set up the equation:
(2.00 mol * 8.314 J/(mol·K) * 1000 K) / V = (5 mol * 8.314 J/(mol·K) * T2) / V
Notice that the volume cancels out, simplifying the equation:
2 * 8.314 * 1000 K = 5 * 8.314 * T2
4. Now, solve for T2, the final temperature:
T2 = (2 * 8.314 * 1000 K) / (5 * 8.314)
T2 ≈ 400 K
Therefore, the final temperature of the gas when the number of moles is increased to 5 moles is approximately 400 K.