The Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas:

PV = nRT

Where:

* P = pressure in atmospheres (atm)

* V = volume in liters (L)

* n = number of moles

* R = ideal gas constant (0.0821 L·atm/mol·K)

* T = temperature in Kelvin (K)

Solving for the Number of Moles (n)

1. Rearrange the Ideal Gas Law equation to solve for n:

n = PV / RT

2. Plug in the given values:

n = (2.62 atm)(47.8 L) / (0.0821 L·atm/mol·K)(775 K)

3. Calculate:

n ≈ 2.08 moles

Therefore, there are approximately 2.08 moles of gas in the container.