a cylinder has a piston at one end that can be moved in or out to change the volume of gas inside. the other end is fitted with a valve. initially the cylinder contains 3.65 mol of an ideal gas. the piston is now pushed in to decrease the volume of gas to two-fifths its initial value without causing any change in temperature. in order to keep the pressure constant as well, how many moles of gas need to be released through the valve?

Avogadro's law stipulates that an equal volume of gases at the same temperature and pressure must contain the same number of molecules. In other words, the total number of atoms or molecules of any gas is directly proportional to the gaseous volume occupied at constant pressure and temperature.

This law can be mathematically expressed as:

[tex]v_1/n_1 = v_2/n_2[/tex]

Where [tex]v_1[/tex] is the initial volume of the gas, [tex]n_1[/tex] is the initial number of moles, [tex]v_2[/tex] is the final volume, and [tex]n_2[/tex] is the final number of moles of the gas.

In this case:

[tex]v_2[/tex] = [tex]2/5v_1[/tex]

[tex]n_1[/tex] = 3.65 mol

The equation can be substituted to give:

[tex]v_1/3.65[/tex] = [tex]0.4v_1/n_2[/tex]

Making [tex]n_2[/tex] the subject:

[tex]n_2[/tex] = 3.65 x 0.4

= 1.46 mol

The final number of moles of the gas in the cylinder should be 1.46. Thus, the number of moles of the gas that needs to be released through the valve would be:

3.65 - 1.46 = 2.19 mol

In other words, 2.19 mol of gas needs to be released through the valve in order to keep the pressure constant.

More on Avogadro's law can be found here: https://brainly.com/question/4133756

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