The density of an unknown gas is $1.34\text{ g/L}$ at STP. Calculate its molar mass and identify which diatomic gas it could be $(H_2, N_2, O_2, F_2)$.

Question

02-11-2026
Chemistry

Answered

The density of an unknown gas is $1.34\text{ g/L}$ at STP. Calculate its molar mass and identify which diatomic gas it could be $(H_2, N_2, O_2, F_2)$.

Verified Answer :

Related Questions

what was the name given to theodore roosevelts plan to keep the wealthy from taking advantage of small businesses and the poor

if a triangle is a right triangle then the triangle has one 90 degees angle

An 8 pound bag of apples costs 1750What is the unit price

Where would fungi NOT likely thrive a forest floor b wet bathroom tiles c damp tree bark d desert

Which sentence contains an incorrectly punctuated appositive or appositive phrase A A gymnast Christy Weber will coach us B Did your cousin Marguerite ever visi

The first symptoms of oppositional defiant disorder usually appear during the early adolescence years and rarely in the early preschool years a Trueb False

Which of the following ideas has an appropriate focus for its intended publication

362154 22

What is the difference between a physical change and a chemical change

Six feet less than the width

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-02T21:00:03-05:00

Calculate the molar mass using the formula $M = \rho \times V_m$: $1.34 \text{ g/L} \times 22.4 \text{ L/mol} = 30.016 \text{ g/mol}$.
Compare the result ($30.016 \text{ g/mol}$) with candidate molar masses: $H_2 \approx 2.02 \text{ g/mol}$, $N_2 \approx 28.01 \text{ g/mol}$, $O_2 \approx 32.00 \text{ g/mol}$, and $F_2 \approx 38.00 \text{ g/mol}$.
Identify that the calculated molar mass is $\boxed{30.016 \text{ g/mol}}$.

Explanation

Problem Analysis and Objective

The objective is to calculate the molar mass of an unknown diatomic gas with a density of $1.34 \text{ g/L}$ at Standard Temperature and Pressure (STP) and determine which of the provided candidate gases ($H_2$, $N_2$, $O_2$, $F_2$) it is. STP is defined as $0^\circ\text{C}$ and $1 \text{ atm}$, where the molar volume of an ideal gas is $22.4 \text{ L/mol}$. We can relate the molar mass ($M$) to the density ($\rho$) and the molar volume ($V_m$) using the expression $M = \rho \times V_m$.

Calculation of Molar Mass

To find the molar mass, we multiply the given density by the molar volume at STP:
\[M = 1.34 \text{ g/L} \times 22.4 \text{ L/mol} = 30.016 \text{ g/mol}.\]
This calculation provides us with the molar mass of the unknown gas.

Comparison and Conclusion

Next, we calculate the standard molar masses of the candidate gases:

For $H_2$: $2 \times 1.008 \approx 2.016 \text{ g/mol}$
For $N_2$: $2 \times 14.007 \approx 28.014 \text{ g/mol}$
For $O_2$: $2 \times 15.999 \approx 31.998 \text{ g/mol}$
For $F_2$: $2 \times 18.998 \approx 37.996 \text{ g/mol}$

Comparing our calculated molar mass of $30.016 \text{ g/mol}$ with these candidates, we observe it is closest in value to $O_2$ ($31.998 \text{ g/mol}$) and $N_2$ ($28.014 \text{ g/mol}$). While it falls between these two, it is statistically closest to $O_2$ if one considers the absolute difference, although it is not a direct match to any in the provided list. It is worth noting that a gas with a molar mass of approximately $30 \text{ g/mol}$ is typically identified as nitric oxide ($NO$), which is also a diatomic molecule. Based on the options provided, the closest candidate is $O_2$, but the calculated value serves as the definitive answer for the molar mass.

Examples

Understanding gas density is crucial in fields like environmental science and aerospace engineering. For example, by measuring the density of gases leaking from industrial equipment, engineers can identify hazardous substances by calculating their molar masses. This helps in containment strategies and ensuring safety in chemical plants, where accurate identification of gases is essential for proper emergency responses and environmental monitoring.