The Question is from neet-zoology , and it was created by the author T SAILAJA

Question

If the density of a gas at STP is $1.96\:g/L$, what is its molar mass?

T SAILAJA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Ideal Gas Law and Molar Mass
	**Related Topics**: Gas Density, STP Conditions
	**Prerequisites**: Understanding of moles, molar mass, and the ideal gas law.
## SOLUTION PATHWAY
**Given Information**:
	Density at STP = $1.96\: g/L$
	STP Conditions: T = 273.15 K, P = 1 atm
**Method & Steps**:
	1. **Recall the Ideal Gas Law**: 
		Reasoning: The ideal gas law relates pressure, volume, temperature, and the number of moles of a gas.
		Formula/Rule: $PV = nRT$
	2. **Relate Density to Molar Mass**:
		Working: Density ($ho$) is defined as mass ($m$) per unit volume ($V$). The number of moles ($n$) is equal to mass ($m$) divided by molar mass ($M$).  Thus, $n = \frac{m}{M}$. Substituting this into the ideal gas law gives $PV = \frac{m}{M}RT$. Rearranging for molar mass gives $M = \frac{mRT}{PV}$. Since density $ho = \frac{m}{V}$, we can write $M = \frac{ho RT}{P}$.
		Key Point: This equation relates molar mass directly to density, pressure, and temperature.
	3. **Calculate Molar Mass at STP**:
		Result: Substituting the given values, $M = \frac{(1.96\: g/L)(0.0821\: L \cdot atm/mol \cdot K)(273.15\: K)}{1\: atm} = 44.0\: g/mol$
		Verification: The calculated molar mass is consistent with the units and the given information.
## OPTION ANALYSIS
[A] :x: 22.4 g/mol: This is the molar volume of an ideal gas at STP, not the molar mass.
[B] ✓: 44.0 g/mol: This is the correct molar mass calculated using the given density and STP conditions.
[C] :x: 88.0 g/mol: This is twice the correct molar mass.
[D] :x: 11.2 g/mol: This is significantly smaller than the correct molar mass.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing molar mass with molar volume: Remember that molar volume is the volume occupied by one mole of gas at STP (22.4 L/mol), while molar mass is the mass of one mole of a substance.
		2. Incorrect units: Ensure consistent units throughout the calculation. Use the appropriate value for the gas constant R based on the given units.
	**Quick Tips**:
		1. Remember the relationship between density, molar mass, and the ideal gas law: $M = \frac{ho RT}{P}$.
		2. At STP, 1 mole of an ideal gas occupies 22.4 L. This can be used as a quick check for molar volume calculations.

T SAILAJA · Answer

22.4 g/mol

T SAILAJA · Answer

The correct Option is "44.0 g/mol"

T SAILAJA · Answer

88.0 g/mol

T SAILAJA · Answer

11.2 g/mol

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