The Question is from neet-chemistry , and it was created by the author CHANDRAKANTH

Question

1.0 L of ${N_2}$ and 7/8 L of ${O_2}$ at the same temperature and pressure were mixed together. What is the relation between the masses of the two gases in the mixture?

CHANDRAKANTH · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Avogadro's Law
	**Related Topics**: Molar Mass, Ideal Gas Law
	**Prerequisites**: Understanding that equal volumes of gases at the same temperature and pressure contain equal number of moles.
## SOLUTION PATHWAY
**Given Information**:
	* Volume of N2 = 1.0 L
	* Volume of O2 = 7/8 L
	* Same Temperature and Pressure
**Method & Steps**:
	1.  Apply Avogadro's Law: At the same temperature and pressure, equal volumes of gases contain equal numbers of moles.
		Reasoning: This law allows us to relate the volumes of the gases to the number of moles.
		Formula/Rule:  $V \propto n$ at constant T and P
	2. Determine the ratio of moles: The ratio of the volumes is the same as the ratio of the number of moles.
		Working: $n_{N_2} : n_{O_2} = 1 : 7/8$.  Therefore, $n_{N_2} = 8/7 n_{O_2}$
		Key Point: We need to find the relation between the masses, not just the moles.
	3. Calculate the ratio of masses: mass (m) = moles (n) * molar mass (M).  Molar mass of N2 = 28 g/mol, Molar mass of O2 = 32 g/mol.
    Working: $m_{N_2} = n_{N_2} * 28$ and $m_{O_2} = n_{O_2} * 32$ . Substituting $n_{N_2} = 8/7 n_{O_2}$  we get  $m_{N_2} = (8/7) n_{O_2} * 28$ =  $32 n_{O_2}$ which is equal to $m_{O_2}$.
		Result: $m_{N_2} = m_{O_2}$
		Verification: The ratio of moles is the inverse ratio of molar mass. This makes the final mass ratio to be 1:1
 ## OPTION ANALYSIS
[A] :x: Incorrect. This ratio is not consistent with the relationship between the volumes and molar masses.
[B] :x: Incorrect. This ratio is not consistent with the relationship between the volumes and molar masses.
[C] ✓: Correct. The mass of N2 is equal to the mass of O2.
[D] :x: Incorrect. This ratio is not consistent with the relationship between the volumes and molar masses.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing volume ratio with mass ratio: The volume ratio directly gives the mole ratio, not the mass ratio. Molar mass must be considered.
		2. Neglecting to consider molar mass: The molar mass is crucial for converting between moles and mass.
	**Quick Tips**:
		1. Remember Avogadro's Law: Equal volumes of gases at the same temperature and pressure have the same number of moles.
		2. Always convert to moles first: When comparing gas quantities at the same conditions, convert to moles before comparing mass.

CHANDRAKANTH · Answer

${M_{\rm{N}}}_2 = 3{M_{\rm{O}}}_2$

CHANDRAKANTH · Answer

${M_{\rm{N}}}_2 = 8{M_{\rm{O}}}_2$

CHANDRAKANTH · Answer

The correct Option is "${M_{\rm{N}}}_2 = {M_{\rm{O}}}_2$"

CHANDRAKANTH · Answer

${M_{\rm{N}}}_2 = 16{M_{\rm{O}}}_2$

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