Calculate The Molar Mass And Atomic Mass Of X X X In 17.75 G Of A Gaseous Compound X 2 O 5 X_2O_5 X 2 ​ O 5 ​ , Which Occupies A Volume Of 2.8 Dm 3 2.8 \, \text{dm}^3 2.8 Dm 3 At STP.Given:- Θ = 16 \theta = 16 Θ = 16 - $v_m , \text{at STP} = 22.4 ,

Introduction

In this article, we will calculate the molar mass and atomic mass of an unknown element $x$ in a gaseous compound $X_2O_5$. The compound occupies a volume of $2.8 \, \text{dm}^3$ at Standard Temperature and Pressure (STP). We will use the given information to determine the molar mass of the compound and then calculate the atomic mass of the unknown element.

Given Information

• Mass of the compound: $17.75 \, \text{g}$
• Volume of the compound: $2.8 \, \text{dm}^3$
• Temperature: $16 \, \text{°C}$
• Pressure: $1 \, \text{atm}$ (STP)
• Molar volume at STP: $22.4 \, \text{dm}^3 \, \text{mol}^{-1}$

Calculating Molar Mass

To calculate the molar mass of the compound, we need to use the formula:

$$\text{Molar Mass} = \frac{\text{Mass of the compound}}{\text{Number of moles of the compound}}$$

First, we need to calculate the number of moles of the compound using the ideal gas equation:

$$\text{Number of moles} = \frac{\text{Volume of the compound}}{\text{Molar volume at STP}}$$

Substituting the given values, we get:

$$\text{Number of moles} = \frac{2.8 \, \text{dm}^3}{22.4 \, \text{dm}^3 \, \text{mol}^{-1}} = 0.125 \, \text{mol}$$

Now, we can calculate the molar mass of the compound:

$$\text{Molar Mass} = \frac{17.75 \, \text{g}}{0.125 \, \text{mol}} = 142.0 \, \text{g} \, \text{mol}^{-1}$$

Calculating Atomic Mass

The molar mass of the compound $X_2O_5$ is the sum of the atomic masses of its constituent elements. Let the atomic mass of the unknown element $x$ be $A_x$. The atomic mass of oxygen is $16 \, \text{g} \, \text{mol}^{-1}$.

The molar mass of the compound can be expressed as:

$$\text{Molar Mass} = 2A_x + 5(16 \, \text{g} \, \text{mol}^{-1})$$

Substituting the calculated molar mass of the compound, we get:

$$142.0 \, \text{g} \, \text{mol}^{-1} = 2A_x + 80 \, \text{g} \, \text{mol}^{-1}$$

Solving for $A_x$, we get:

$$A_x = \frac{142.0 \, \text{g} \, \text{mol}^{-1} - 80 \, \text{g} \, \text{mol}^{-1}}{2} = 31.0 \, \text{g} \, \text{mol}^{-1}$$

Therefore, the atomic mass of the unknown element $x$ is $31.0 \, \text{g} \, \text{mol}^{-1}$.

Conclusion

In this article, we calculated the molar mass and atomic mass of an unknown element $x$ in a gaseous compound $X_2O_5$. We used the given information to determine the molar mass of the compound and then calculated the atomic mass of the unknown element. The atomic mass of the unknown element $x$ is $31.0 \, \text{g} \, \text{mol}^{-1}$.

References

• Ideal Gas Equation: $PV = nRT$
• Molar Volume at STP: $22.4 \, \text{dm}^3 \, \text{mol}^{-1}$
• Atomic Mass of Oxygen: $16 \, \text{g} \, \text{mol}^{-1}$
  Q&A: Calculating Molar Mass and Atomic Mass of a Gaseous Compound ====================================================================

Frequently Asked Questions

Q: What is the molar mass of the compound $X_2O_5$?

A: The molar mass of the compound $X_2O_5$ is $142.0 \, \text{g} \, \text{mol}^{-1}$.

Q: How do I calculate the number of moles of the compound?

A: To calculate the number of moles of the compound, you can use the ideal gas equation: $\text{Number of moles} = \frac{\text{Volume of the compound}}{\text{Molar volume at STP}}$.

Q: What is the atomic mass of the unknown element $x$?

A: The atomic mass of the unknown element $x$ is $31.0 \, \text{g} \, \text{mol}^{-1}$.

Q: How do I calculate the atomic mass of the unknown element $x$?

A: To calculate the atomic mass of the unknown element $x$, you can use the formula: $A_x = \frac{\text{Molar Mass} - 5(16 \, \text{g} \, \text{mol}^{-1})}{2}$.

Q: What is the significance of the molar mass and atomic mass of the compound and its constituent elements?

A: The molar mass and atomic mass of the compound and its constituent elements are important in chemistry as they help us understand the properties and behavior of the compound and its constituent elements.

Q: How do I apply the ideal gas equation to calculate the number of moles of the compound?

A: To apply the ideal gas equation, you need to know the volume of the compound, the molar volume at STP, and the temperature and pressure of the gas. You can then use the equation: $\text{Number of moles} = \frac{\text{Volume of the compound}}{\text{Molar volume at STP}}$.

Q: What is the relationship between the molar mass of the compound and the atomic masses of its constituent elements?

A: The molar mass of the compound is the sum of the atomic masses of its constituent elements. In the case of the compound $X_2O_5$, the molar mass is $2A_x + 5(16 \, \text{g} \, \text{mol}^{-1})$.

Q: How do I determine the atomic mass of the unknown element $x$ from the molar mass of the compound?

A: To determine the atomic mass of the unknown element $x$, you can use the formula: $A_x = \frac{\text{Molar Mass} - 5(16 \, \text{g} \, \text{mol}^{-1})}{2}$.

Q: What are the limitations of the ideal gas equation in calculating the number of moles of the compound?

A: The ideal gas equation assumes that the gas is ideal, which means that it does not account for the interactions between the gas molecules. In reality, the gas may not behave ideally, which can affect the accuracy of the calculation.

Q: How do I account for the limitations of the ideal gas equation in calculating the number of moles of the compound?

A: To account for the limitations of the ideal gas equation, you can use more advanced equations that take into account the interactions between the gas molecules. However, these equations are more complex and may require more information about the gas.

Conclusion

In this Q&A article, we have answered some of the frequently asked questions about calculating the molar mass and atomic mass of a gaseous compound. We have discussed the ideal gas equation, the relationship between the molar mass of the compound and the atomic masses of its constituent elements, and the limitations of the ideal gas equation. We hope that this article has been helpful in understanding the concepts and calculations involved in determining the molar mass and atomic mass of a gaseous compound.