What Is The Percent By Mass Of Sodium In N A 2 S O 4 Na_2SO_4 N A 2 S O 4 ?Use The Formula: % Element = ( Total mass of element in compound Molar mass of compound ) × 100 \% \text{Element} = \left( \frac{\text{total Mass Of Element In Compound}}{\text{molar Mass Of Compound}} \right) \times 100 % Element = ( Molar mass of compound Total mass of element in compound ) × 100 A. 16.18 % 16.18\% 16.18% B.

Mar 13, 2025 by ADMIN 410 views

What is the Percent by Mass of Sodium in $Na_2SO_4$ ?

Understanding the Problem

To find the percent by mass of sodium in $Na_2SO_4$ , we need to calculate the total mass of sodium in the compound and then divide it by the molar mass of the compound. The formula to calculate the percent by mass of an element in a compound is given by:

$\% \text{Element} = \left( \frac{\text{total mass of element in compound}}{\text{molar mass of compound}} \right) \times 100$

Calculating the Molar Mass of $Na_2SO_4$

The molar mass of a compound is the sum of the atomic masses of its constituent elements. The atomic masses of sodium (Na), sulfur (S), and oxygen (O) are 22.99 g/mol, 32.07 g/mol, and 16.00 g/mol, respectively.

The molar mass of $Na_2SO_4$ can be calculated as follows:

Molar mass of $Na_2SO_4$ = (2 x atomic mass of Na) + atomic mass of S + (4 x atomic mass of O) = (2 x 22.99 g/mol) + 32.07 g/mol + (4 x 16.00 g/mol) = 45.98 g/mol + 32.07 g/mol + 64.00 g/mol = 142.05 g/mol

Calculating the Total Mass of Sodium in $Na_2SO_4$

The total mass of sodium in $Na_2SO_4$ is the sum of the atomic masses of the two sodium atoms in the compound.

Total mass of sodium = 2 x atomic mass of Na = 2 x 22.99 g/mol = 45.98 g/mol

Calculating the Percent by Mass of Sodium in $Na_2SO_4$

Now that we have the total mass of sodium and the molar mass of $Na_2SO_4$ , we can calculate the percent by mass of sodium in the compound using the formula:

$\% \text{Sodium} = \left( \frac{\text{total mass of sodium}}{\text{molar mass of compound}} \right) \times 100$ = $\left( \frac{45.98 \text{ g/mol}}{142.05 \text{ g/mol}} \right) \times 100$ = 0.324 or 32.4%

Conclusion

Therefore, the percent by mass of sodium in $Na_2SO_4$ is 32.4%. This means that sodium makes up approximately 32.4% of the mass of $Na_2SO_4$ .

Answer

The correct answer is B. 32.4%.

Discussion

This problem requires the application of the formula for calculating the percent by mass of an element in a compound. The student must first calculate the molar mass of the compound and then the total mass of the element in the compound. Finally, the student must divide the total mass of the element by the molar mass of the compound and multiply by 100 to get the percent by mass of the element.

Tips and Tricks

Make sure to calculate the molar mass of the compound correctly by summing the atomic masses of its constituent elements.
Use the correct formula to calculate the percent by mass of the element.
Check your units to ensure that they are consistent throughout the calculation.

Related Problems

What is the percent by mass of sulfur in $Na_2SO_4$ ?
What is the percent by mass of oxygen in $Na_2SO_4$ ?
What is the molar mass of $Na_2SO_4$ ?

Conclusion

In conclusion, the percent by mass of sodium in $Na_2SO_4$ is 32.4%. This problem requires the application of the formula for calculating the percent by mass of an element in a compound. The student must first calculate the molar mass of the compound and then the total mass of the element in the compound. Finally, the student must divide the total mass of the element by the molar mass of the compound and multiply by 100 to get the percent by mass of the element.
Q&A: Percent by Mass of Elements in Compounds

Q: What is the percent by mass of sodium in $Na_2SO_4$ ?

A: The percent by mass of sodium in $Na_2SO_4$ is 32.4%. This means that sodium makes up approximately 32.4% of the mass of $Na_2SO_4$ .

Q: How do I calculate the percent by mass of an element in a compound?

A: To calculate the percent by mass of an element in a compound, you need to follow these steps:

Calculate the molar mass of the compound by summing the atomic masses of its constituent elements.
Calculate the total mass of the element in the compound.
Divide the total mass of the element by the molar mass of the compound.
Multiply the result by 100 to get the percent by mass of the element.

Q: What is the formula for calculating the percent by mass of an element in a compound?

A: The formula for calculating the percent by mass of an element in a compound is:

$\% \text{Element} = \left( \frac{\text{total mass of element in compound}}{\text{molar mass of compound}} \right) \times 100$

Q: How do I calculate the molar mass of a compound?

A: To calculate the molar mass of a compound, you need to sum the atomic masses of its constituent elements. For example, the molar mass of $Na_2SO_4$ is calculated as follows:

Q: What is the percent by mass of sulfur in $Na_2SO_4$ ?

A: The percent by mass of sulfur in $Na_2SO_4$ is 22.5%. This means that sulfur makes up approximately 22.5% of the mass of $Na_2SO_4$ .

Q: What is the percent by mass of oxygen in $Na_2SO_4$ ?

A: The percent by mass of oxygen in $Na_2SO_4$ is 45.1%. This means that oxygen makes up approximately 45.1% of the mass of $Na_2SO_4$ .

Q: How do I apply the formula for calculating the percent by mass of an element in a compound?

A: To apply the formula, you need to follow these steps:

Calculate the molar mass of the compound.
Calculate the total mass of the element in the compound.
Divide the total mass of the element by the molar mass of the compound.
Multiply the result by 100 to get the percent by mass of the element.

Q: What are some common mistakes to avoid when calculating the percent by mass of an element in a compound?

A: Some common mistakes to avoid when calculating the percent by mass of an element in a compound include:

Calculating the molar mass of the compound incorrectly.
Failing to calculate the total mass of the element in the compound.
Dividing the total mass of the element by the molar mass of the compound incorrectly.
Multiplying the result by 100 incorrectly.

Q: How do I check my work when calculating the percent by mass of an element in a compound?

A: To check your work, you can follow these steps:

Review your calculations to ensure that you have calculated the molar mass of the compound correctly.
Review your calculations to ensure that you have calculated the total mass of the element in the compound correctly.
Review your calculations to ensure that you have divided the total mass of the element by the molar mass of the compound correctly.
Review your calculations to ensure that you have multiplied the result by 100 correctly.

Conclusion

In conclusion, calculating the percent by mass of an element in a compound requires careful attention to detail and a thorough understanding of the formula. By following the steps outlined in this article, you can ensure that you calculate the percent by mass of an element in a compound accurately.