.10 mol of Argon gas is admitted to an evacuated 50cm cubed container at 20 degrees celsius. The gas then undergoes an isobaric heating to a temperature of 300 degrees celsius. What is the final volume of the gas?

To solve this problem, we can use the ideal gas law, which states that 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.

First, let's convert the temperature from degrees Celsius to Kelvin by adding 273.15.
The initial temperature is 20 degrees Celsius, so the initial temperature in Kelvin is:
T1 = 20 + 273.15 = 293.15 K

The final temperature is 300 degrees Celsius, so the final temperature in Kelvin is:
T2 = 300 + 273.15 = 573.15 K

Since the gas is isobarically heated, the pressure remains constant throughout the process.

Next, let's calculate the initial volume of the gas. We are given that the initial volume is 50 cm³, which we need to convert to liters.
V1 = 50 cm³ × (1 L / 1000 cm³) = 0.05 L

Now, let's use the ideal gas law formula to find the final volume of the gas:
(P1 × V1) / T1 = (P2 × V2) / T2

Since the pressure is constant, we can cancel it out:
V1 / T1 = V2 / T2

Now we can rearrange the formula to solve for V2, the final volume:
V2 = (V1 / T1) × T2

Substituting the values we found:
V2 = (0.05 L / 293.15 K) × 573.15 K

Calculating this:
V2 = 0.0977 L

Therefore, the final volume of the gas is approximately 0.0977 liters.

To find the final volume of the gas after isobaric heating, we can use the combined gas law. The combined gas law relates the initial and final conditions of the gas.

The combined gas law is given by the equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:
P1 and P2 are the initial and final pressures respectively
V1 and V2 are the initial and final volumes respectively
T1 and T2 are the initial and final temperatures respectively, measured in Kelvin

Let's calculate step by step:

Step 1: Convert the initial and final temperatures from Celsius to Kelvin.

T1 = 20 degrees Celsius + 273.15 = 293.15 K
T2 = 300 degrees Celsius + 273.15 = 573.15 K

Step 2: Determine the initial volume V1 and pressure P1.
Given:
Initial volume V1 = 50 cm³
Initial moles n = 0.10 mol
To find the initial pressure P1, we can use the ideal gas law:

PV = nRT

Where:
P is the pressure
V is the volume (in liters)
n is the number of moles of gas
R is the ideal gas constant, which is 0.0821 L·atm/(mol·K)
T is the temperature in Kelvin

Since we have the volume in cm³, we need to convert it to liters:

V1 = 50 cm³ / 1000 = 0.05 L

Now we can calculate the initial pressure P1:

P1 = (n * R * T1) / V1

P1 = (0.10 mol * 0.0821 L·atm/(mol·K) * 293.15 K) / 0.05 L

Step 3: Calculate the final volume V2.
To find the final volume V2, rearrange the combined gas law equation and solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We don't have the final pressure P2, but since the process is isobaric (constant pressure), P1 = P2. Therefore, we can simplify the equation to:

V2 = (V1 * T2) / T1

Now we can plug in the values:

V2 = (0.05 L * 573.15 K) / 293.15 K

Solving this equation will give us the final volume V2.

The issue here in my mind is the chamber fixed volume or not? I don't know how one evacuates a chamber that can change size. If it is fixed, the volume remains at 50ml.