There are three main gas laws. Avogadro’s law states that the moles of a gas is directly proportional to the volume (under constant pressure and temperature). Boyle’s law states that the pressure of the gas is inversely proportional to the volume (under constant moles and temperature). This means that the pressure decreases proportionally when the volume increases. Charles’ law states that the temperature is directly proportional to the volume (under constant moles and pressure). The question states that the piston moves up. This means that the volume of the gas is expanding inside and pushing the piston up to make room for the expanding gas. The gas expansion occurs due to increased temperature (Charles’ law).

First, we need to figure out which gas law is applicable here. The question states that temperature and moles are constant. This means that we are dealing with Boyle’s law, which states that pressure is inversely proportional to volume. Inversely proportional means that the pressure decreases as volume increases and vice versa. Note that the relationship is still linear (change in one variable causes a proportional change in the other variable), but the two variables have a negative correlation. Positive correlation means increasing or decreasing a variable would also increase or decrease the other variable, respectively. 

Recall that Charles’ law defines the relationship between temperature and volume at constant pressure and constant moles. The law states that the two variables are directly proportional to each other. This means that increasing or decreasing temperature will have the same effect on volume. This makes sense because increasing the temperature increases the kinetic energy of the particles. This makes it easier for particles to move away from each other and expand, which results in an increase in volume.

To solve this question we need to use the ideal gas law equation:

Above,  is pressure in ,  is volume in liters,  is moles,  is , and  is temperature in Kelvins. The question gives us pressure, volume, and temperature; therefore, we can solve for . First, we need to convert temperature from Celsius to Kelvins.

Rearrange the ideal gas law and solve for :

The question states that you place one gram of gas in the container. Since we know the moles, we can solve for the molecular weight of the gas and figure out its identity from the molecular weight.

The molecular weight of oxygen gas,  is ; therefore, the unknown gas must be oxygen.

The argon gas, as the problem states, is under constant temperature with varying volume and pressure, so we need to use Boyle's Law:

We are given the initial pressure, the initial volume, and the final pressure, and need to solve for the final volume. Therefore, we can rearrange Boyle's law to be as follows: 

Plug in known values and solve.

The methane gas, as the problem states, is under constant temperature with varying volume and pressure, so we need to use Boyle's Law:

We are given the initial pressure, the initial volume, and the final volume and need to solve for the final pressure. Therefore, we can rearrange Boyle's law to be as follows:

Plug in known values and solve.