A cylinder contains 0.1 cubic meters of gas at atmospheric pressure. This gas is allowed to expand until its pressure drops to 7800 Pa. What is the gas volume after this expansion has taken place?
answer: 7800/10130 = 0.770
To solve this problem, we'll use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature of the gas in Kelvin
In this case, we know the initial volume (0.1 cubic meters) and the initial pressure (atmospheric pressure). We're trying to find the final volume after the gas expands and the pressure drops to 7800 Pa.
First, let's convert the initial pressure from atmospheric pressure to Pascals:
1 atm = 101325 Pa
So, the initial pressure is 101325 Pa.
Now, we can set up the initial equation using the given data:
(101325 Pa) * (0.1 cubic meters) = n * (8.314 J/(mol·K)) * T
The temperature (T) is not explicitly given, but since the problem does not mention any changes in temperature, we can assume that it remains constant.
Now, let's rearrange the equation to solve for n (number of moles):
n = (101325 Pa * 0.1 cubic meters) / (8.314 J/(mol·K) * T)
Next, we can rearrange the ideal gas law equation to solve for the final volume (V):
V = (n * (8.314 J/(mol·K)) * T) / 7800 Pa
Now, substitute the expression for n into the equation:
V = ((101325 Pa * 0.1 cubic meters) / (8.314 J/(mol·K) * T)) * (8.314 J/(mol·K)) * T / 7800 Pa
Simplifying the equation:
V = (101325 * 0.1 / 7800) cubic meters
V = 0.130 cubic meters (rounded to three decimal places)
So, the gas volume after the expansion is approximately 0.130 cubic meters.