To solve the problem, we need to determine the volume of CH₄ gas adsorbed per gram of charcoal at a pressure of 608 torr and a temperature of 27°C. Here’s a step-by-step solution:
### Step 1: Calculate the initial volume of CH₄ gas at 760 torr
Using the ideal gas law, we can find the volume of gas at the initial pressure (P₁ = 760 torr) and the volume of the vessel (V = 1 L).
\[
V_1 = 1 \, \text{L} = 1000 \, \text{mL}
\]
### Step 2: Calculate the final volume of CH₄ gas at 608 torr
Using the formula for the relationship between pressure and volume (Boyle's Law), we can find the final volume (V₂) of the gas when the pressure drops to 608 torr:
\[
P_1 \cdot V_1 = P_2 \cdot V_2
\]
Substituting the known values:
\[
760 \, \text{torr} \cdot 1000 \, \text{mL} = 608 \, \text{torr} \cdot V_2
\]
Now, solving for V₂:
\[
V_2 = \frac{760 \cdot 1000}{608} \approx 1250 \, \text{mL}
\]
### Step 3: Calculate the volume of charcoal
To find the volume occupied by the charcoal, we can use its mass and density. The density of charcoal is given as 1.6 g/cm³.
\[
\text{Volume of charcoal} = \frac{\text{mass}}{\text{density}} = \frac{16 \, \text{g}}{1.6 \, \text{g/cm}^3} = 10 \, \text{cm}^3 = 10 \, \text{mL}
\]
### Step 4: Calculate the volume of CH₄ gas adsorbed
The volume of CH₄ gas adsorbed can be calculated by subtracting the volume occupied by the charcoal from the final volume of the gas:
\[
\text{Volume of gas adsorbed} = V_2 - \text{Volume of charcoal} = 1250 \, \text{mL} - 10 \, \text{mL} = 1240 \, \text{mL}
\]
### Step 5: Calculate the volume of CH₄ gas adsorbed per gram of charcoal
Now we can find the volume of CH₄ gas adsorbed per gram of charcoal:
\[
\text{Volume of gas adsorbed per gram} = \frac{\text{Volume of gas adsorbed}}{\text{mass of charcoal}} = \frac{1240 \, \text{mL}}{16 \, \text{g}} = 77.5 \, \text{mL/g}
\]
### Final Answer
The volume of CH₄ gas adsorbed per gram of charcoal at 608 torr and 27°C is **77.5 mL/g**.
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