Sure, let's go through the solution step-by-step.
### Step 1: Analyze Compound A
We are given the mass of Sodium (Na) and element Z in compound A:
- Mass of Na (in A): [tex]\(12.00\)[/tex] grams
- Mass of Z (in A): [tex]\(2.44\)[/tex] grams
Since the formula for compound A is [tex]\( \text{Na}_3 \text{Z} \)[/tex], the molar ratio of Na to Z can be represented as the ratio of their masses:
[tex]\[
\text{Molar Mass Ratio of Na to Z in A} = \frac{\text{Mass of Na}}{\text{Mass of Z}} = \frac{12.00}{2.44}
\][/tex]
### Step 2: Examine Compound B
We are given the mass of Sodium (Na) and element Z in Compound B:
- Mass of Na (in B): [tex]\(3.45\)[/tex] grams
- Mass of Z (in B): [tex]\(0.700\)[/tex] grams
Since we aim to use the same molar ratio for consistency, we can calculate the mass of Z in Compound B using the given intact values.
### Step 3: Determine Mass of Z in Compound C
For Compound C, we know:
- Mass of Na (in C): [tex]\(14.00\)[/tex] grams
- Formula: [tex]\( \text{Na}_3 \text{Z} \)[/tex]
Since the compound forms the same molar ratio as in Compound A, to find the mass of Z in Compound C, we use:
[tex]\[
\text{Mass of Z (in C)} = \frac{\text{Mass of Na (in C)}}{\text{Molar Mass Ratio of Na to Z in A}}
\][/tex]
### Step 4: Given Data for Compound D
- Mass of Na (in D): [tex]\(25.00\)[/tex] grams
- Mass of Z (in D): [tex]\(30.47\)[/tex] grams
Since these values are provided, we don't need any further calculations for Compound D.
### Calculated Results
Summarizing the calculated masses of element Z:
1. Compound A:
[tex]\[
\text{Mass of Z} = 2.44 \, \text{grams}
\][/tex]
2. Compound B:
[tex]\[
\text{Mass of Z} = 0.700 \, \text{grams}
\][/tex]
3. Compound C:
[tex]\[
\text{Mass of Z} = 2.8466666666666667 \, \text{grams}
\][/tex]
4. Compound D:
[tex]\[
\text{Mass of Z} = 30.47 \, \text{grams}
\][/tex]
Thus, from the provided data and calculations:
- For Compound A, the mass of Z is [tex]\(2.44\)[/tex] grams.
- For Compound B, the mass of Z is [tex]\(0.700\)[/tex] grams.
- For Compound C, the calculated mass of Z is [tex]\(2.8466666666666667\)[/tex] grams.
- For Compound D, the mass of Z is [tex]\(30.47\)[/tex] grams.
Hence, the mass of element Z in each specified compound is correctly calculated in a consistent manner, preserving the ratio consistent with Compound A.
