57.7 g Ni contains how many atoms?

To find the number of atoms in 57.7 grams of nickel (Ni), we use the formula:

[ \text{Number of atoms} = \left( \frac{\text{mass in grams}}{\text{molar mass of the element}} \right) \times \text{Avogadro's number} ]

Nickel's molar mass is approximately 58.69 g/mol, and Avogadro's number is (6.022 \times 10^{23}) atoms/mol.

[ \text{Number of atoms} = \left( \frac{57.7 \text{ g}}{58.69 \text{ g/mol}} \right) \times 6.022 \times 10^{23} \text{ atoms/mol} ]

[ \text{Number of atoms} \approx \left( 0.983 \text{ mol} \right) \times 6.022 \times 10^{23} \text{ atoms/mol} ]

[ \text{Number of atoms} \approx 5.92 \times 10^{23} \text{ atoms} ]

Therefore, 57.7 grams of nickel contains approximately (5.92 \times 10^{23}) atoms.

To determine the number of atoms in 57.7 grams of nickel (Ni), we'll use the following steps:

1. Find the molar mass of nickel (Ni) from the periodic table. Nickel has an atomic mass of approximately 58.69 grams per mole (g/mol).

2. Convert the given mass of nickel (57.7 grams) to moles using the formula: [ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} ]

3. Once we have the number of moles, we can use Avogadro's constant, which states that there are (6.022 \times 10^{23}) atoms in one mole of a substance.

4. Multiply the number of moles by Avogadro's constant to find the number of atoms.

Let's calculate: [ \text{Molar mass of Ni} = 58.69 , \text{g/mol} ] [ \text{moles of Ni} = \frac{57.7 , \text{g}}{58.69 , \text{g/mol}} ] [ \text{moles of Ni} \approx 0.983 , \text{moles} ]

[ \text{Number of atoms} = \text{moles} \times 6.022 \times 10^{23} ] [ \text{Number of atoms} \approx 0.983 , \text{moles} \times 6.022 \times 10^{23} , \text{atoms/mol} ] [ \text{Number of atoms} \approx 5.92 \times 10^{23} , \text{atoms} ]

Therefore, 57.7 grams of nickel contains approximately (5.92 \times 10^{23}) atoms.