The relationship between the number of molecules, temperature, and pressure of a gas is described by the ideal gas law, which states:
PV = nRT
Where: P is the pressure of the gas, V is the volume of the gas, n is the number of molecules (or moles) of the gas, R is the ideal gas constant, and T is the temperature of the gas.
If we keep the volume constant (V is fixed) and double the number of molecules (n doubles), we can examine the effect on pressure (P). Rearranging the ideal gas law, we have:
P = (nRT) / V
If we double n while keeping V and R constant, the equation becomes:
P' = (2nRT) / V = 2P
This means that doubling the number of molecules in a fixed volume of gas will result in the gas having double the pressure, as long as the temperature (T) and the volume (V) remain constant.
It's important to note that this relationship assumes an ideal gas behavior, where there are no intermolecular forces or other factors that could affect the behavior of the gas molecules. In reality, the behavior of real gases may deviate from the ideal gas law under certain conditions.