To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where: P = pressure V = volume n = number of moles R = ideal gas constant (8.314 J/(mol·K)) T = temperature
We can assume the number of moles (n) remains constant during the compression process, so we can rewrite the equation as:
P₁V₁ / T₁ = P₂V₂ / T₂
Where: P₁ = initial pressure (98 mmHg) V₁ = initial volume (2 L) T₁ = initial temperature (25°C + 273.15 K = 298.15 K) P₂ = final pressure (unknown) V₂ = final volume (0.1 L) T₂ = final temperature (3°C + 273.15 K = 276.15 K)
Now, we can rearrange the equation to solve for P₂:
P₂ = (P₁V₁T₂) / (V₂T₁)
Substituting the given values:
P₂ = (98 mmHg * 2 L * 276.15 K) / (0.1 L * 298.15 K)
Note: We need to convert the pressure to the same unit system, so 1 mmHg is equal to 133.322 Pascal (Pa).
P₂ = (98 mmHg * 2 L * 276.15 K) / (0.1 L * 298.15 K) = (98 * 133.322 Pa * 2 L * 276.15 K) / (0.1 L * 298.15 K) = 9084.79 Pa
Therefore, the pressure required to compress 2L of gas at 98 mmHg pressure and 25°C into a container of 0.1L capacity at a temperature of 3°C is approximately 9084.79 Pa.