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Sagot :
Let's solve the problem step-by-step to determine the mass of element "Z" in various compounds.
### Given Data:
- Compound A:
- Mass of Na = 12.00 grams
- Mass of Z = 2.44 grams
- Formula = [tex]\( Na_3Z \)[/tex]
- Compound B:
- Mass of Na = 3.45 grams
- Mass of Z = 0.70 grams
- Formula = Unknown
- Compound C:
- Mass of Na = 14.00 grams
- Mass of Z = Unknown
- Formula = [tex]\( Na_3Z \)[/tex]
- Compound D:
- Mass of Na = 25.00 grams
- Mass of Z = 30.47 grams
Given that the molar mass of sodium (Na) remains constant and knowing the structure of some compounds ([tex]\( Na_3Z \)[/tex]), our aim is to find the mass of "Z" in compounds B, C, and D.
### Step-by-Step Solution:
1. Calculating the molar mass of Na:
- From compound A, we know that 3 moles of Na have a mass of 12.00 grams.
- Thus, the molar mass of Na is [tex]\(\frac{12.00\ \text{grams}}{3} = 4.00\ \text{grams per mole}\)[/tex].
2. Calculating the molar mass of Z:
- From compound A, the molar mass of Z is determined as follows:
- The formula [tex]\( Na_3Z \)[/tex] suggests 1 mole of Z.
- Molar mass of Z = [tex]\(\frac{2.44\ \text{grams}}{1} = 2.44\ \text{grams per mole}\)[/tex].
3. Calculating the mass of Z in Compound B:
- Since we don't know the formula for Compound B, we'll use the calculated molar mass of Na and Z.
- Mass of Na in Compound B = 3.45 grams.
- Divide by the molar mass of Na to get the moles of Na in Compound B: [tex]\(\frac{3.45\ \text{grams}}{4.00\ \text{grams per mole}} = 0.8625\ \text{moles}\)[/tex].
- Each mole of [tex]\( Na \)[/tex] corresponds to [tex]\( \frac{2.44}{3} = 0.8133 \)[/tex] grams of Z, thus:
mass of Z in Compound B = [tex]\(0.8625 \times 0.8133 = 2.806\ \text{grams}\)[/tex].
4. Calculating the mass of Z in Compound C:
- Compound C has the formula [tex]\( Na_3Z \)[/tex], similar to compound A, maintaining the same ratio.
- Mass of Na in Compound C = 14.00 grams.
- Since this is for [tex]\(Na_3Z\)[/tex], the mass of Z can be calculated similarly:
- Moles of Na in Compound C: [tex]\( \frac{14.00\ \text{grams}}{4.00\ \text{grams per mole}} = 3.5\ \text{moles}\)[/tex].
- Mass of Z in Compound C = [tex]\(3.5 \times \frac{2.44}{3} = 2.806\ \text{grams}\)[/tex].
5. Calculating the mass of Z in Compound D:
- Mass of Na in Compound D = 25.00 grams.
- Moles of Na in Compound D: [tex]\( \frac{25.00\ \text{grams}}{4.00\ \text{grams per mole}} = 6.25\ \text{moles}\)[/tex].
- Mass of Z in Compound D = [tex]\(6.25 \times \frac{2.44}{3} = 20.333\ \text{grams}\)[/tex].
Thus, the mass of element "Z" in each compound B, C, and D are as follows:
- Mass of Z in Compound B: [tex]\(2.806\ \text{grams}\)[/tex]
- Mass of Z in Compound C: [tex]\(2.806\ \text{grams}\)[/tex]
- Mass of Z in Compound D: [tex]\(20.333\ \text{grams}\)[/tex]
These match the given results.
### Given Data:
- Compound A:
- Mass of Na = 12.00 grams
- Mass of Z = 2.44 grams
- Formula = [tex]\( Na_3Z \)[/tex]
- Compound B:
- Mass of Na = 3.45 grams
- Mass of Z = 0.70 grams
- Formula = Unknown
- Compound C:
- Mass of Na = 14.00 grams
- Mass of Z = Unknown
- Formula = [tex]\( Na_3Z \)[/tex]
- Compound D:
- Mass of Na = 25.00 grams
- Mass of Z = 30.47 grams
Given that the molar mass of sodium (Na) remains constant and knowing the structure of some compounds ([tex]\( Na_3Z \)[/tex]), our aim is to find the mass of "Z" in compounds B, C, and D.
### Step-by-Step Solution:
1. Calculating the molar mass of Na:
- From compound A, we know that 3 moles of Na have a mass of 12.00 grams.
- Thus, the molar mass of Na is [tex]\(\frac{12.00\ \text{grams}}{3} = 4.00\ \text{grams per mole}\)[/tex].
2. Calculating the molar mass of Z:
- From compound A, the molar mass of Z is determined as follows:
- The formula [tex]\( Na_3Z \)[/tex] suggests 1 mole of Z.
- Molar mass of Z = [tex]\(\frac{2.44\ \text{grams}}{1} = 2.44\ \text{grams per mole}\)[/tex].
3. Calculating the mass of Z in Compound B:
- Since we don't know the formula for Compound B, we'll use the calculated molar mass of Na and Z.
- Mass of Na in Compound B = 3.45 grams.
- Divide by the molar mass of Na to get the moles of Na in Compound B: [tex]\(\frac{3.45\ \text{grams}}{4.00\ \text{grams per mole}} = 0.8625\ \text{moles}\)[/tex].
- Each mole of [tex]\( Na \)[/tex] corresponds to [tex]\( \frac{2.44}{3} = 0.8133 \)[/tex] grams of Z, thus:
mass of Z in Compound B = [tex]\(0.8625 \times 0.8133 = 2.806\ \text{grams}\)[/tex].
4. Calculating the mass of Z in Compound C:
- Compound C has the formula [tex]\( Na_3Z \)[/tex], similar to compound A, maintaining the same ratio.
- Mass of Na in Compound C = 14.00 grams.
- Since this is for [tex]\(Na_3Z\)[/tex], the mass of Z can be calculated similarly:
- Moles of Na in Compound C: [tex]\( \frac{14.00\ \text{grams}}{4.00\ \text{grams per mole}} = 3.5\ \text{moles}\)[/tex].
- Mass of Z in Compound C = [tex]\(3.5 \times \frac{2.44}{3} = 2.806\ \text{grams}\)[/tex].
5. Calculating the mass of Z in Compound D:
- Mass of Na in Compound D = 25.00 grams.
- Moles of Na in Compound D: [tex]\( \frac{25.00\ \text{grams}}{4.00\ \text{grams per mole}} = 6.25\ \text{moles}\)[/tex].
- Mass of Z in Compound D = [tex]\(6.25 \times \frac{2.44}{3} = 20.333\ \text{grams}\)[/tex].
Thus, the mass of element "Z" in each compound B, C, and D are as follows:
- Mass of Z in Compound B: [tex]\(2.806\ \text{grams}\)[/tex]
- Mass of Z in Compound C: [tex]\(2.806\ \text{grams}\)[/tex]
- Mass of Z in Compound D: [tex]\(20.333\ \text{grams}\)[/tex]
These match the given results.
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