The variation of volume of an ideal gas with its number of moles (\( n \)) is obtained as a graph at 300 K and 1 atm pressure. What is the slope of the graph?
\( 24.6 \) L
\( 24.6 \) L mol\(^{-1}\)
Step 1: Use the Ideal Gas Equation
The ideal gas equation is: \[ PV = nRT \] where: - \( P \) is the pressure (1 atm), - \( V \) is the volume, - \( n \) is the number of moles, - \( R \) is the universal gas constant (\( 0.0821 \) L atm mol\(^{-1}\) K\(^{-1}\)), - \( T \) is the temperature (300 K).
Step 2: Express Volume as a Function of \( n \)
Rearranging the equation: \[ V = \frac{nRT}{P} \] Since \( R = 0.0821 \), \( T = 300 \) K, and \( P = 1 \) atm: \[ V = \frac{(n)(0.0821)(300)}{1} \] \[ V = 24.6 n \]
Step 3: Identify the Slope
The equation is in the form: \[ V = m n \] where \( m \) (the slope) is 24.6 L mol\(^{-1}\).
Step 4: Verify the Correct Answer
Thus, the slope of the graph is \( 24.6 \) L mol\(^{-1}\), which matches Option (2).
At 400 K, the following graph is obtained for \( x \) moles of an ideal gas. \( x \) is equal to (R = gas constant, P = pressure, V = volume)
The following graph is obtained for the adsorption of a gas on the surface of a catalyst. The values of k and n are respectively
Observe the following reactions (not balanced):
Cl2 + NaOH → NaCl + X + H2O
Cl2 + NaOH → NaCl + Y + H2O
Which of the following is not correct?
(1) XeO2 is a colorless explosive gas
(2) SO2 is highly soluble in water
(3) Noble gases have very low boiling points
(4) The boiling point of sulphur is more than that of oxygen