Consider two different containers, each filled with 2 moles of Ne(g). One of the containers is rigid and has constant volume. The other container is flexible (like a balloon) and is capable of changing its volume to keep the external pressure and internal pressure equal to each other. If you raise the temperature in both containers, what happens to the pressure and density of the gas inside each container? Assume a constant external pressure.

The ideal gas law is given by: \( PV = nRT \) Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in kelvin.

Since the volume of the rigid container is constant, we can use the ideal gas law to find the effect of increasing the temperature on the pressure and density of the gas. The density of the gas is given by: \( \rho = \frac{m}{V} = \frac{nM}{V} \) Where M is the molar mass of the gas. Since the volume and moles remain constant and the temperature increases: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \) As the temperature increases, the pressure will also increase, which can be seen from the equation above. Since the volume is constant, the density of the gas will remain the same in the rigid container.

In the flexible container, the external pressure (P) and internal pressure are equal to each other and remain constant. Again, we can use the ideal gas law to investigate the effect of increasing the temperature on the pressure and density of the gas. Since the pressure is constant and the temperature increases: \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \) As the temperature increases, the volume of the gas in the flexible container will also increase, which can be seen from the equation above. Now let's analyze the density of the gas in the flexible container. Since the molar mass, moles, and temperature are constant, we can rewrite the equation for the density change as: \( \rho_1 = \frac{nM}{V_1} \) and \( \rho_2 = \frac{nM}{V_2} \) As the volume increases (due to the temperature increase), the density of the gas in the flexible container will decrease.

In the rigid container, when the temperature increases, the pressure will increase, and the density will remain the same. In the flexible container, when the temperature increases, the pressure will remain the same, and the density will decrease.