Understanding the Concepts

* Ideal Gas Law: The ideal gas law describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of an ideal gas: PV = nRT.

* Constant Volume: Since the container is rigid, the volume (V) remains constant.

* Direct Proportionality: The ideal gas law shows that pressure (P) is directly proportional to temperature (T) when volume (V) and moles (n) are constant.

Calculations

1. Convert Temperatures to Kelvin:

* 2°C + 273.15 = 275.15 K

* 10°C + 273.15 = 283.15 K

2. Set up a Proportion:

Since volume and moles are constant, we can write:

P₁/T₁ = P₂/T₂

Where:

* P₁ = Initial pressure (3.0 atm)

* T₁ = Initial temperature (275.15 K)

* P₂ = Final pressure (unknown)

* T₂ = Final temperature (283.15 K)

3. Solve for P₂:

* P₂ = (P₁ * T₂) / T₁

* P₂ = (3.0 atm * 283.15 K) / 275.15 K

* P₂ ≈ 3.09 atm

Answer

The pressure in the container will increase to approximately 3.09 atmospheres when the temperature is raised to 10 degrees Celsius.