To solve the problem of finding the total pressure exerted by a mixture of gases in a 5-liter flask, we will follow these steps:
### Step 1: Calculate the moles of each gas.
**For Nitrogen (N₂):**
- Given mass = 3.5 g
- Molar mass of N₂ = 28 g/mol (since N = 14 g/mol, and N₂ = 2 × 14)
\[
\text{Moles of N₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{3.5 \, \text{g}}{28 \, \text{g/mol}} = 0.125 \, \text{mol}
\]
**For Hydrogen (H₂):**
- Given mass = 3 g
- Molar mass of H₂ = 2 g/mol (since H = 1 g/mol, and H₂ = 2 × 1)
\[
\text{Moles of H₂} = \frac{3 \, \text{g}}{2 \, \text{g/mol}} = 1.5 \, \text{mol}
\]
**For Oxygen (O₂):**
- Given mass = 8 g
- Molar mass of O₂ = 32 g/mol (since O = 16 g/mol, and O₂ = 2 × 16)
\[
\text{Moles of O₂} = \frac{8 \, \text{g}}{32 \, \text{g/mol}} = 0.25 \, \text{mol}
\]
### Step 2: Calculate the total moles of gas.
\[
\text{Total moles} = \text{Moles of N₂} + \text{Moles of H₂} + \text{Moles of O₂}
\]
\[
\text{Total moles} = 0.125 + 1.5 + 0.25 = 1.875 \, \text{mol}
\]
### Step 3: Convert the temperature from Celsius to Kelvin.
Given temperature = 27°C
\[
\text{Temperature in Kelvin} = 27 + 273 = 300 \, \text{K}
\]
### Step 4: Use the Ideal Gas Law to calculate the total pressure.
The Ideal Gas Law is given by:
\[
PV = nRT
\]
Where:
- \( P \) = pressure (atm)
- \( V \) = volume (L)
- \( n \) = number of moles (mol)
- \( R \) = universal gas constant = 0.0821 L·atm/(K·mol)
- \( T \) = temperature (K)
Rearranging for pressure \( P \):
\[
P = \frac{nRT}{V}
\]
Substituting the values:
\[
P = \frac{(1.875 \, \text{mol}) \times (0.0821 \, \text{L·atm/(K·mol)}) \times (300 \, \text{K})}{5 \, \text{L}}
\]
Calculating:
\[
P = \frac{(1.875) \times (0.0821) \times (300)}{5}
\]
\[
P = \frac{46.125375}{5} = 9.225075 \, \text{atm}
\]
### Step 5: Round the answer.
The total pressure exerted by the mixture of gases is approximately:
\[
P \approx 9.24 \, \text{atm}
\]
### Final Answer:
The total pressure exerted by the mixture of gases is **9.24 atm**.
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