To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where: P = pressure V = volume n = number of moles of gas R = ideal gas constant (8.314 J/(mol·K)) T = temperature
We need to find the new gas pressure (P₂) after adding 2.8 g of gas to the original 10.9 g sample, while keeping the volume constant at 5.25 L and raising the temperature to 65 ∘C.
Step 1: Calculate the initial number of moles of gas (n₁) using the given data for the initial sample.
n₁ = (mass₁) / (molar mass) n₁ = (10.9 g) / (molar mass of the gas)
Step 2: Calculate the final number of moles of gas (n₂) after adding 2.8 g of gas.
n₂ = n₁ + (mass₂) / (molar mass) n₂ = n₁ + (2.8 g) / (molar mass of the gas)
Step 3: Calculate the new gas pressure (P₂) using the ideal gas law.
P₂ = (n₂ * R * T₂) / V
Now let's plug in the values and solve the equation.
Given data: Initial mass (mass₁) = 10.9 g Final mass after adding (mass₂) = 2.8 g Volume (V) = 5.25 L Temperature (T₁) = 26 ∘C = 26 + 273.15 K = 299.15 K Final temperature (T₂) = 65 ∘C = 65 + 273.15 K = 338.15 K
Step 1: Calculate n₁ n₁ = (10.9 g) / (molar mass of the gas)
Step 2: Calculate n₂ n₂ = n₁ + (2.8 g) / (molar mass of the gas)
Step 3: Calculate P₂ P₂ = (n₂ * R * T₂) / V
By solving these steps, we can find the new gas pressure, P₂.