Question:
The density of methane is maximum under which conditions?
The density of methane is maximum under which conditions?
Show Hint
For an ideal gas,
\[
d=\frac{PM}{RT}
\]
Density is directly proportional to pressure and inversely proportional to temperature.
Updated On: Jun 18, 2026
- \(0^\circ C,\ 2\ \text{bar}\)
- \(273^\circ C,\ 1\ \text{bar}\)
- \(273^\circ C,\ 2\ \text{bar}\)
- \(0^\circ C,\ 3\ \text{bar}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Use the density relation for an ideal gas.
The density of a gas is given by \[ d=\frac{PM}{RT} \] where \[ P=\text{pressure}, \quad M=\text{molar mass}, \quad R=\text{gas constant}, \quad T=\text{temperature} \] For methane, \(M\) and \(R\) are constant.
Therefore, \[ d\propto \frac{P}{T} \]
Step 2: Analyze the effect of pressure and temperature.
Density increases with increase in pressure.
Density decreases with increase in temperature.
Hence, maximum density will occur at the highest pressure and the lowest temperature.
Step 3: Compare the given options.
Among the given options: \[ 0^\circ C = 273\ K \] and \[ 273^\circ C = 546\ K \] The lowest temperature is \[ 0^\circ C \] and the highest pressure is \[ 3\ \text{bar} \] Therefore, the maximum value of \[ \frac{P}{T} \] occurs for \[ 0^\circ C,\ 3\ \text{bar} \]
Step 4: Final conclusion.
Hence, methane has maximum density at \[ \boxed{0^\circ C,\ 3\ \text{bar}} \] Therefore, the correct option is (4).
The density of a gas is given by \[ d=\frac{PM}{RT} \] where \[ P=\text{pressure}, \quad M=\text{molar mass}, \quad R=\text{gas constant}, \quad T=\text{temperature} \] For methane, \(M\) and \(R\) are constant.
Therefore, \[ d\propto \frac{P}{T} \]
Step 2: Analyze the effect of pressure and temperature.
Density increases with increase in pressure.
Density decreases with increase in temperature.
Hence, maximum density will occur at the highest pressure and the lowest temperature.
Step 3: Compare the given options.
Among the given options: \[ 0^\circ C = 273\ K \] and \[ 273^\circ C = 546\ K \] The lowest temperature is \[ 0^\circ C \] and the highest pressure is \[ 3\ \text{bar} \] Therefore, the maximum value of \[ \frac{P}{T} \] occurs for \[ 0^\circ C,\ 3\ \text{bar} \]
Step 4: Final conclusion.
Hence, methane has maximum density at \[ \boxed{0^\circ C,\ 3\ \text{bar}} \] Therefore, the correct option is (4).
Was this answer helpful?
0
0
Top AP EAPCET Chemistry Questions
- The four quantum numbers of the valence electron of potassium are :
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
- In which of the following the election gain enthalpy of elements is correctly arranged?
- The radii of $ \text{F,}{{\text{F}}^{-}}\text{O} $ and $ {{\text{O}}^{2-}} $ are in the order
- Which of the following has the highest first ionization potential?
View More Questions
Top AP EAPCET Gas laws Questions
Two statements are given below: Statement-I: The ratio of the molar volume of a gas to that of an ideal gas at constant temperature and pressure is called the compressibility factor.
Statement-II: The RMS velocity of a gas is directly proportional to the square root of \( T(K) \).- Identify the correct statements from the following:
(I) According to Charles' law, at constant pressure, the volume of a gas is directly proportional to its temperature.
(II) The rate of diffusion of a certain mass of a gas is inversely proportional to its density, at constant pressure and temperature.
(III) The kinetic energy of a gas is directly proportional to T (K). - At 300 K, 1 g of an ideal gas (A) exerted a pressure of 2 atm in a closed container. When 2 g of another ideal gas (B) was introduced into this container at the same temperature, the pressure changed to 3 atm. The correct relationship between the molar mass of A (\(M_A\)) and B (\(M_B\)) is:
- The vapors of 1 g of an element occupy 2.5625 L exerting a pressure of 0.5 atm at 1000 K. What is the molar mass (in $\text{g mol}^{-1}$) of the element? (Assume vapors follow ideal gas equation. Given $R = 0.082 \text{ L atm mol}^{-1} \text{K}^{-1}$)
- A gas obeys Charles' law in the temperature range 0--500 K at a given pressure. Its volume changes to zero at temperature of
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions