A gas occupies a 1.5 liter container at 250C and 2.0 atmospheres. If the gas is transferred to a 3.0 liter container at the same temperature, what will be the new pressure?

To find the new pressure, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Since we're keeping the temperature constant, we can rewrite the equation as:

P1V1 = P2V2

Where:
P1 = initial pressure
V1 = initial volume
P2 = new pressure
V2 = new volume

Given:
P1 = 2.0 atmospheres
V1 = 1.5 liters
V2 = 3.0 liters

Substituting the given values into the equation, we have:

(2.0 atm)(1.5 L) = (P2)(3.0 L)

Simplifying the equation, we get:

3.0 atm * L = 2.0 atm * 1.5 L

Dividing both sides by 3.0 L, we have:

P2 = (2.0 atm * 1.5 L) / 3.0 L

P2 = 1.0 atm

Therefore, the new pressure in the 3.0 liter container at the same temperature will be 1.0 atmospheres.

To find the new pressure of the gas when transferred to a different container, we can use the combined gas law equation:

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

Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure (what we want to find)
V2 = Final volume (which is given)
T2 = Final temperature (which is the same as the initial temperature in this case)

We are given:
P1 = 2.0 atmospheres
V1 = 1.5 liters
T1 = 25°C (we will convert this to Kelvin later)
V2 = 3.0 liters
T2 = T1 (same temperature)

First, we need to convert the temperature from Celsius to Kelvin by adding 273.15.
T1 = 25°C + 273.15 = 298.15 K

Now we can substitute these values into the equation:
(2.0 atm * 1.5 L) / (298.15 K) = (P2 * 3.0 L) / (298.15 K)

Rearranging the equation to solve for P2:
P2 = (2.0 atm * 1.5 L * 298.15 K) / (3.0 L)

Simplifying:
P2 = 2.0 atm * 1.5 * 298.15 K / 3.0

P2 = 447.225 atm * K / L

Thus, the new pressure when the gas is transferred to the 3.0 liter container at the same temperature will be approximately 447.225 atmospheres.