15 Find the relative atomic mass of nickel if 3.370 g
nickel was obtained by reduction of 4.286 g of
the oxide (NiO). You may need to refer to the periodic
table at the end of this book.

Question

15 Find the relative atomic mass of nickel if 3.370 g nickel was obtained by reduction of 4.286 g of the oxide (NiO). You may need to refer to the periodic table at the end of this book.

UpStudy AI · Accepted Answer

**Step 1. Write the composition of the oxide**

The oxide of nickel is given as $$ \text{NiO} $$. Its molar mass is  
$$
M_{\text{NiO}} = M_{\text{Ni}} + 16
$$
where $$ M_{\text{Ni}} $$ is the atomic mass of nickel.

**Step 2. Establish the mass fraction of nickel in $$ \text{NiO} $$**

The mass fraction of nickel is  
$$
\frac{M_{\text{Ni}}}{M_{\text{Ni}} + 16}
$$

**Step 3. Set up the equation using the given masses**

We are told that 4.286 g of $$ \text{NiO} $$ yields 3.370 g of nickel. This means the fraction of nickel in the sample is  
$$
\frac{3.370}{4.286}
$$
Equate the two fractions:
$$
\frac{M_{\text{Ni}}}{M_{\text{Ni}} + 16} = \frac{3.370}{4.286}
$$

**Step 4. Solve the equation for $$ M_{\text{Ni}} $$**

Multiply both sides by $$ M_{\text{Ni}} + 16 $$:
$$
M_{\text{Ni}} = \frac{3.370}{4.286} (M_{\text{Ni}} + 16)
$$

Multiply both sides by 4.286:
$$
4.286\,M_{\text{Ni}} = 3.370\,M_{\text{Ni}} + 3.370 \times 16
$$

Compute $$ 3.370 \times 16 $$:
$$
3.370 \times 16 = 53.92
$$
Thus:
$$
4.286\,M_{\text{Ni}} = 3.370\,M_{\text{Ni}} + 53.92
$$

Subtract $$ 3.370\,M_{\text{Ni}} $$ from both sides:
$$
(4.286 - 3.370) M_{\text{Ni}} = 53.92
$$
$$
0.916\,M_{\text{Ni}} = 53.92
$$

Solve for $$ M_{\text{Ni}} $$:
$$
M_{\text{Ni}} = \frac{53.92}{0.916} \approx 58.9
$$

**Step 5. Conclude**

The relative atomic mass of nickel is approximately  
$$
\boxed{58.9}
$$
The relative atomic mass of nickel is approximately 58.9.

15 Find the relative atomic mass of nickel if 3.370 g
nickel was obtained by reduction of 4.286 g of
the oxide (NiO). You may need to refer to the periodic
table at the end of this book.

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