determine the number of grams of Ne gas that must be added to a container in order for the volume to increase to 38.2 L at constant pressure and temperature if the container had an initial volume of 25.0 L and 2.0 moles of Ne

The shorter way to work this is harder to explain so let me show you the long way. First assume a value for T, use PV = nRT, and solve for P.

P = ?
V = 25.0L
n = 2 mols (we'll call this n1)
R -= 0.08206
T = 273.

After you get P, use PV = nRT again. Use the same valus for R, T, and the value you obtained for P. Solve for n = how many mols must be in the container. Call that n2.
So how many mols Ne must be added. That's n2-n2 = ? and convert to grams. g = mols x molar mass.

1.72

To determine the number of grams of Ne gas that must be added to the container, we first need to calculate the moles of Ne gas in the initial volume. Then, we can use the ideal gas law to find the number of moles in the final volume. Finally, we can convert the moles to grams using the molar mass of Ne.

1. Calculate the moles of Ne gas in the initial volume:
Given that the initial volume is 25.0 L and there are 2.0 moles of Ne gas, we can use the formula:
Moles = Volume / 22.4 (at STP, 1 mole of gas occupies 22.4 L)
Moles = 25.0 L / 22.4 L/mol
Moles = 1.12 moles

2. Use the ideal gas law to calculate the moles in the final volume:
The ideal gas law formula is: PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is temperature in Kelvin.
Since the pressure and temperature are constant in this problem, we can set up the following equation:
(P_initial * V_initial) / (n_initial * T_initial) = (P_final * V_final) / (n_final * T_final)
Plugging in the known values:
(2.0 moles * 25.0 L) / (1 * T_initial) = (2.0 moles * 38.2 L) / (n_final * T_final)
Simplifying the equation:
(50.0 L) / T_initial = (76.4 L) / (n_final * T_final)
(50.0 L * n_final * T_final) = (76.4 L * T_initial)
n_final = (76.4 L * T_initial) / (50.0 L * T_final)
n_final = 1.52 moles

3. Convert moles to grams:
We can use the molar mass of Ne (20.18 g/mol) to convert moles to grams:
Grams = Moles * Molar mass
Grams = 1.52 moles * 20.18 g/mol
Grams = 30.68 g

Therefore, you need to add approximately 30.68 grams of Ne gas to the container to increase the volume to 38.2 L at constant pressure and temperature.