sample of gas at 17°C from a volume of 5.68 L and 1.10 atm to a container at 37°C that has a pressure of 1.10 atm. What is the new volume of gas?
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of temperature, volume, and pressure of the gas.
The combined gas law formula is as follows:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (in atm)
V1 = initial volume (in L)
T1 = initial temperature (in Kelvin)
P2 = final pressure (in atm)
V2 = final volume (in L)
T2 = final temperature (in Kelvin)
In this case, we have:
P1 = 1.10 atm (initial pressure)
V1 = 5.68 L (initial volume)
T1 = 17°C (initial temperature)
P2 = 1.10 atm (final pressure)
V2 = ? (final volume, what we want to find)
T2 = 37°C (final temperature)
First, we need to convert the initial and final temperatures to Kelvin. The Kelvin temperature scale starts at absolute zero, which is -273.15°C. So, we can convert Celsius to Kelvin by adding 273.15.
T1 = 17°C + 273.15 = 290.15 K
T2 = 37°C + 273.15 = 310.15 K
Now, we can plug the values into the combined gas law formula:
(1.10 atm * 5.68 L) / (290.15 K) = (1.10 atm * V2) / (310.15 K)
To find V2, we can rearrange the equation:
(1.10 atm * V2) = (1.10 atm * 5.68 L) * (310.15 K) / (290.15 K)
Now, let's solve the equation:
V2 = (1.10 atm * 5.68 L) * (310.15 K) / (290.15 K * 1.10 atm)
V2 = 5.97 L
Therefore, the new volume of gas is approximately 5.97 L.