The intercept on y-axis and slope of curve plotted between P/T vs. T
( For an ideal gas having 10 moles in a closed rigid container of volume 8.21 L. (P= Pressure in atm and T = Temp. in K, `log_(10)2=0.30))` are respectively :

Options

A. 0.01, 0
B. 0.1, 0
C. 0.1, 1
D. 10, 1

Explanation

To solve the problem, we need to analyze the relationship between pressure (P), temperature (T), and the number of moles (n) of an ideal gas using the ideal gas law. Let's break it down step by step.

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = Pressure (in atm)
- \( V \) = Volume (in L)
- \( n \) = Number of moles
- \( R \) = Ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = Temperature (in K)

### Step 2: Rearranging the Ideal Gas Law
We need to express \( P/T \) in terms of \( T \):
From the ideal gas law, we can rearrange it as:
\[ P = \frac{nRT}{V} \]
Dividing both sides by \( T \):
\[ \frac{P}{T} = \frac{nR}{V} \]
This shows that \( \frac{P}{T} \) is a constant (since \( n \), \( R \), and \( V \) are constants).

### Step 3: Plotting the Graph
We are asked to plot \( P/T \) against \( T \). This can be expressed in the form of a linear equation:
\[ \frac{P}{T} = \frac{nR}{V} \]
This can be rewritten as:
\[ \frac{P}{T} = 0 \cdot T + \frac{nR}{V} \]
Where:
- The slope (m) = 0
- The y-intercept (c) = \( \frac{nR}{V} \)

### Step 4: Calculate the Intercept
Now, we need to calculate the intercept \( c \):
Given:
- \( n = 10 \) moles
- \( R = 0.0821 \) L·atm/(K·mol)
- \( V = 8.21 \) L

Substituting these values into the intercept formula:
\[ c = \frac{nR}{V} = \frac{10 \times 0.0821}{8.21} \]

Calculating:
\[ c = \frac{0.821}{8.21} \]
\[ c = 0.1 \]

### Step 5: Determine the Slope
From our earlier analysis, we found that the slope \( m = 0 \).

### Final Answer
Thus, the intercept on the y-axis is \( 0.1 \) and the slope of the curve is \( 0 \). Therefore, the answer is:
**Intercept: 0.1, Slope: 0**