Answer :
To find the mass in grams of [tex]\(1.64 \times 10^{20}\)[/tex] molecules of [tex]\(C_6H_{12}O_6\)[/tex] (glucose), we need to follow these steps:
1. Understand the Conversion Factors Needed:
- Avogadro's Number: This number, approximately [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many molecules there are in one mole of a substance.
- Molar Mass of Glucose ([tex]\(C_6H_{12}O_6\)[/tex]): The molar mass is 180.18 grams per mole.
2. Convert Molecules to Moles:
- We know that [tex]\(1.64 \times 10^{20}\)[/tex] molecules are given.
- To find out how many moles this is, divide the number of molecules by Avogadro's number:
[tex]\[
\text{moles of glucose} = \frac{1.64 \times 10^{20}}{6.022 \times 10^{23}}
\][/tex]
3. Calculate the Mass in Grams:
- Once you know the number of moles, multiply the moles by the molar mass of glucose to find the mass:
[tex]\[
\text{mass in grams} = \text{moles of glucose} \times 180.18
\][/tex]
After performing these steps, the calculations yield:
- The number of moles of glucose molecules is approximately [tex]\(0.00027233\)[/tex] moles.
- The mass of [tex]\(1.64 \times 10^{20}\)[/tex] molecules of glucose is approximately [tex]\(0.0491\)[/tex] grams.
So, the answer is about 0.0491 grams.
1. Understand the Conversion Factors Needed:
- Avogadro's Number: This number, approximately [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many molecules there are in one mole of a substance.
- Molar Mass of Glucose ([tex]\(C_6H_{12}O_6\)[/tex]): The molar mass is 180.18 grams per mole.
2. Convert Molecules to Moles:
- We know that [tex]\(1.64 \times 10^{20}\)[/tex] molecules are given.
- To find out how many moles this is, divide the number of molecules by Avogadro's number:
[tex]\[
\text{moles of glucose} = \frac{1.64 \times 10^{20}}{6.022 \times 10^{23}}
\][/tex]
3. Calculate the Mass in Grams:
- Once you know the number of moles, multiply the moles by the molar mass of glucose to find the mass:
[tex]\[
\text{mass in grams} = \text{moles of glucose} \times 180.18
\][/tex]
After performing these steps, the calculations yield:
- The number of moles of glucose molecules is approximately [tex]\(0.00027233\)[/tex] moles.
- The mass of [tex]\(1.64 \times 10^{20}\)[/tex] molecules of glucose is approximately [tex]\(0.0491\)[/tex] grams.
So, the answer is about 0.0491 grams.
