The pressure of 6.0 L of an ideal gas in a flexible container is decreased to one-half of its original pressure, and its absolute temperature is decreased to one-seventh of the original. What is the final volume of the gas?

PV=nRT

v= nRT/P

It looks to me as t= 1/7 To and P is 1/2 Po

V= nRTo*2/7Po or volume is 2/7 of 6 liters.

To find the final volume of the gas, we can use the combined gas law, which states:

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

Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure
V2 = Final volume (what we want to find)
T2 = Final temperature

Given:
P1 = Original pressure
V1 = 6.0 L
T1 = Original temperature
P2 = One-half of the original pressure = 1/2 * P1
T2 = One-seventh of the original temperature = 1/7 * T1

Substituting these values into the combined gas law, we get:

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

Plugging in the given values, we have:

(P1 * 6.0) / T1 = ((1/2 * P1) * V2) / (1/7 * T1)

Simplifying, we get:

6.0 = (1/2) * (V2) * (7/1)

6.0 = (7/2) * (V2)

To solve for V2, divide both sides by (7/2):

V2 = 6.0 / (7/2)

V2 = 6.0 * (2/7)

V2 = 12/7

Therefore, the final volume of the gas is 12/7 L.

To find the final volume of the gas, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature.

The combined gas law formula is:

(P1 × V1) / T1 = (P2 × V2) / T2

Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature

P2 = Final pressure
V2 = Final volume (what we're trying to find)
T2 = Final temperature

In this problem, we are given:
P1 = initial pressure
V1 = initial volume = 6.0 L
T1 = initial temperature

We are also given:
P2 = final pressure = 1/2 of initial pressure
T2 = final temperature = 1/7 of initial temperature

Let's substitute the known values into the combined gas law equation:

(P1 × V1) / T1 = (P2 × V2) / T2

(P1 × 6.0) / T1 = ([1/2P1] × V2) / (1/7T1)

Simplifying this equation, we can cancel out P1 and T1:

6.0 / 1 = (1/2 × V2) / 1/7

6.0 = (1/2 × V2) × 7

Now, we can solve for V2 by multiplying both sides by 2/7:

V2 = (6.0 × 2) / 7
V2 = 12.0 / 7
V2 = 1.71 L

Therefore, the final volume of the gas is approximately 1.71 L.