Answer :
To find out how many grams are in [tex]\(1.57 \times 10^{31}\)[/tex] molecules of [tex]\( \text{MgBr}_2 \)[/tex], follow these steps:
1. Determine the Molar Mass of [tex]\( \text{MgBr}_2 \)[/tex]:
- Magnesium (Mg) has an atomic mass of 24.305 g/mol.
- Bromine (Br) has an atomic mass of 79.904 g/mol, and there are two bromine atoms in magnesium bromide.
So, the molar mass of [tex]\( \text{MgBr}_2 \)[/tex] can be calculated as:
[tex]\[
\text{Molar mass of } \text{MgBr}_2 = 24.305 + (79.904 \times 2) = 184.113 \text{ g/mol}
\][/tex]
2. Use Avogadro's Number:
Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole. This number helps in converting molecules to moles.
3. Calculate the Number of Moles:
To find out how many moles correspond to [tex]\(1.57 \times 10^{31}\)[/tex] molecules, use the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}
\][/tex]
Substitute the values:
[tex]\[
\text{Number of moles} = \frac{1.57 \times 10^{31}}{6.022 \times 10^{23}} \approx 26071072.733 \text{ moles}
\][/tex]
4. Calculate Mass in Grams:
To find the mass in grams, multiply the number of moles by the molar mass of [tex]\( \text{MgBr}_2 \)[/tex]:
[tex]\[
\text{Mass (grams)} = \text{Number of moles} \times \text{Molar mass of } \text{MgBr}_2
\][/tex]
[tex]\[
\text{Mass (grams)} = 26071072.733 \times 184.113 \approx 4800023414.148 \text{ grams}
\][/tex]
Therefore, there are approximately 4,800,023,414 grams in [tex]\(1.57 \times 10^{31}\)[/tex] molecules of [tex]\( \text{MgBr}_2 \)[/tex].
1. Determine the Molar Mass of [tex]\( \text{MgBr}_2 \)[/tex]:
- Magnesium (Mg) has an atomic mass of 24.305 g/mol.
- Bromine (Br) has an atomic mass of 79.904 g/mol, and there are two bromine atoms in magnesium bromide.
So, the molar mass of [tex]\( \text{MgBr}_2 \)[/tex] can be calculated as:
[tex]\[
\text{Molar mass of } \text{MgBr}_2 = 24.305 + (79.904 \times 2) = 184.113 \text{ g/mol}
\][/tex]
2. Use Avogadro's Number:
Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole. This number helps in converting molecules to moles.
3. Calculate the Number of Moles:
To find out how many moles correspond to [tex]\(1.57 \times 10^{31}\)[/tex] molecules, use the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}
\][/tex]
Substitute the values:
[tex]\[
\text{Number of moles} = \frac{1.57 \times 10^{31}}{6.022 \times 10^{23}} \approx 26071072.733 \text{ moles}
\][/tex]
4. Calculate Mass in Grams:
To find the mass in grams, multiply the number of moles by the molar mass of [tex]\( \text{MgBr}_2 \)[/tex]:
[tex]\[
\text{Mass (grams)} = \text{Number of moles} \times \text{Molar mass of } \text{MgBr}_2
\][/tex]
[tex]\[
\text{Mass (grams)} = 26071072.733 \times 184.113 \approx 4800023414.148 \text{ grams}
\][/tex]
Therefore, there are approximately 4,800,023,414 grams in [tex]\(1.57 \times 10^{31}\)[/tex] molecules of [tex]\( \text{MgBr}_2 \)[/tex].
