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Answer :
To solve this problem, we need to determine the total mass of the compound [tex]\( A_2X \)[/tex] that contains 44.1 grams of element [tex]\( A \)[/tex]. Here's a step-by-step breakdown of how we can find the solution:
1. Understand the information given:
- The compound [tex]\( A_2X \)[/tex] is 36.9% [tex]\( A \)[/tex] by mass. This means that in every 100 grams of the compound, 36.9 grams is the element [tex]\( A \)[/tex].
2. Set up the relationship:
- We need to find the total mass of the compound [tex]\( A_2X \)[/tex] that contains 44.1 grams of [tex]\( A \)[/tex].
3. Use the percentage to calculate total mass:
- The mass of [tex]\( A \)[/tex] is given as 44.1 grams, and it constitutes 36.9% of the total mass of the compound.
- To find the total mass of the compound, set up the equation:
[tex]\[
\text{Mass of } A = \left(\frac{\text{Percentage of } A}{100}\right) \times \text{Total mass of compound}
\][/tex]
- Plug in the known values to solve for the total mass of the compound:
[tex]\[
44.1 = \left(\frac{36.9}{100}\right) \times \text{Total mass of compound}
\][/tex]
4. Solve for the total mass of the compound:
- Rearrange the equation to isolate the total mass of the compound:
[tex]\[
\text{Total mass of compound} = \frac{44.1}{36.9 / 100} = \frac{44.1}{0.369}
\][/tex]
5. Calculate the final result:
- Perform the division to find the total mass of the compound:
[tex]\[
\text{Total mass of compound} = 119.51
\][/tex]
- Round the result to the nearest whole number to match the answer choices provided. The total mass of the compound is approximately 120 grams.
Therefore, the mass of the compound [tex]\( A_2X \)[/tex] that contains 44.1 grams of [tex]\( A \)[/tex] is 120 grams.
1. Understand the information given:
- The compound [tex]\( A_2X \)[/tex] is 36.9% [tex]\( A \)[/tex] by mass. This means that in every 100 grams of the compound, 36.9 grams is the element [tex]\( A \)[/tex].
2. Set up the relationship:
- We need to find the total mass of the compound [tex]\( A_2X \)[/tex] that contains 44.1 grams of [tex]\( A \)[/tex].
3. Use the percentage to calculate total mass:
- The mass of [tex]\( A \)[/tex] is given as 44.1 grams, and it constitutes 36.9% of the total mass of the compound.
- To find the total mass of the compound, set up the equation:
[tex]\[
\text{Mass of } A = \left(\frac{\text{Percentage of } A}{100}\right) \times \text{Total mass of compound}
\][/tex]
- Plug in the known values to solve for the total mass of the compound:
[tex]\[
44.1 = \left(\frac{36.9}{100}\right) \times \text{Total mass of compound}
\][/tex]
4. Solve for the total mass of the compound:
- Rearrange the equation to isolate the total mass of the compound:
[tex]\[
\text{Total mass of compound} = \frac{44.1}{36.9 / 100} = \frac{44.1}{0.369}
\][/tex]
5. Calculate the final result:
- Perform the division to find the total mass of the compound:
[tex]\[
\text{Total mass of compound} = 119.51
\][/tex]
- Round the result to the nearest whole number to match the answer choices provided. The total mass of the compound is approximately 120 grams.
Therefore, the mass of the compound [tex]\( A_2X \)[/tex] that contains 44.1 grams of [tex]\( A \)[/tex] is 120 grams.
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