To determine the mass, in grams, of a 0.274 mole sample of nickel (II) acetate, Ni(C2H3O2)2, we need to follow these steps:
1. Identify the molar masses of each element in the compound:
- Nickel (Ni): Molar mass = 58.69 g/mol
- Carbon (C): Molar mass = 12.01 g/mol
- Hydrogen (H): Molar mass = 1.008 g/mol
- Oxygen (O): Molar mass = 16.00 g/mol
2. Determine the number of each type of atom in one formula unit of nickel (II) acetate:
- Ni = 1 atom
- C = 4 atoms (2 atoms per acetate group × 2 acetate groups)
- H = 6 atoms (3 atoms per acetate group × 2 acetate groups)
- O = 4 atoms (2 atoms per acetate group × 2 acetate groups)
3. Calculate the molar mass of nickel (II) acetate:
[tex]\[
\text{Molar mass of Ni(C}_2\text{H}_3\text{O}_2\text{)$_2$} = (1 \times 58.69) + (4 \times 12.01) + (6 \times 1.008) + (4 \times 16.00)
\][/tex]
Substituting the values and performing the calculations:
[tex]\[
= 58.69 + (4 \times 12.01) + (6 \times 1.008) + (4 \times 16.00)
\][/tex]
[tex]\[
= 58.69 + 48.04 + 6.048 + 64.00
\][/tex]
Summing these values gives us:
[tex]\[
= 176.778 \text{ g/mol}
\][/tex]
4. Use the molar mass to convert moles to grams:
To determine the mass of 0.274 moles of nickel (II) acetate, multiply the number of moles by the molar mass:
[tex]\[
\text{Mass in grams} = \text{moles} \times \text{molar mass}
\][/tex]
Substituting the given values:
[tex]\[
\text{Mass in grams} = 0.274 \text{ moles} \times 176.778 \text{ g/mol}
\][/tex]
Performing the multiplication:
[tex]\[
\text{Mass in grams} = 48.437172 \text{ g}
\][/tex]
Therefore, a 0.274 mole sample of nickel (II) acetate, Ni(C2H3O2)2, has a mass of approximately 48.437 grams.
