In an adsorption experiment, a graph of log(x/m) versus log P was found to be linear with a slope of 45°, and the the intercept of of 0.3010. The amount of gas adsorbed per gram charcoal under a pressure of 0.8 bar is

Options

A. 1.2
B. 1.4
C. 1.6
D. 1.8

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship
The relationship between the amount of gas adsorbed (x/m) and pressure (P) can be expressed using the equation:
\[ \log\left(\frac{x}{m}\right) = \log k + \frac{1}{n} \log P \]
Where:
- \(x\) is the amount of gas adsorbed,
- \(m\) is the mass of the charcoal,
- \(P\) is the pressure,
- \(k\) is the intercept,
- \(n\) is a constant related to the adsorption process.

### Step 2: Identify the given values
From the problem, we have:
- Slope (1/n) = 1 (since the slope is 45°)
- Intercept (log k) = 0.3010
- Pressure (P) = 0.8 bar

### Step 3: Calculate \(n\)
Since the slope is 1, we can find \(n\):
\[ \frac{1}{n} = 1 \implies n = 1 \]

### Step 4: Substitute the values into the equation
Now we can substitute the values into the equation:
\[ \log\left(\frac{x}{m}\right) = 0.3010 + 1 \cdot \log(0.8) \]

### Step 5: Calculate \(\log(0.8)\)
Using logarithm properties, we find:
\[ \log(0.8) \approx -0.096 (using a calculator or logarithm table) \]

### Step 6: Substitute \(\log(0.8)\) back into the equation
Now substituting this value back:
\[ \log\left(\frac{x}{m}\right) = 0.3010 - 0.096 \]
\[ \log\left(\frac{x}{m}\right) = 0.205 \]

### Step 7: Find \(x/m\) by taking the antilog
To find \(x/m\), we take the antilog:
\[ \frac{x}{m} = 10^{0.205} \approx 1.58 \]

### Step 8: Round the answer
Rounding to two decimal places gives:
\[ \frac{x}{m} \approx 1.6 \]

### Final Answer
The amount of gas adsorbed per gram of charcoal under a pressure of 0.8 bar is approximately **1.6**.

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