To determine the temperature of the gas at 2.30 ATM, we can use the combined gas law, which relates the initial and final conditions of a gas sample.
The combined gas law is expressed as:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
where P₁, V₁, and T₁ represent the initial pressure, volume, and temperature, respectively, and P₂, V₂, and T₂ represent the final pressure, volume, and temperature, respectively.
Given: P₁ = 1.10 ATM (initial pressure) T₁ = 28.5 °C (initial temperature) P₂ = 2.30 ATM (final pressure)
We need to determine T₂ (final temperature).
First, we need to convert the initial temperature from Celsius to Kelvin: T₁(K) = T₁(°C) + 273.15 T₁(K) = 28.5 °C + 273.15 = 301.65 K
Now we can rearrange the combined gas law equation to solve for T₂:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
T₂ = (P₂ × V₂ × T₁) / (P₁ × V₁)
Since the volume is held constant, V₂ = V₁, the equation simplifies to:
T₂ = (P₂ / P₁) × T₁
Substituting the values:
T₂ = (2.30 ATM / 1.10 ATM) × 301.65 K T₂ ≈ 632.86 K
Finally, we convert the temperature from Kelvin back to Celsius:
T₂(°C) = T₂(K) - 273.15 T₂(°C) ≈ 632.86 K - 273.15 ≈ 359.71 °C
Therefore, the temperature of the gas at 2.30 ATM is approximately 359.71 °C.