Answer :
To determine how many molecules of ethane ([tex]$C_2H_6$[/tex]) are present in 64.28 liters of ethane gas at standard temperature and pressure (STP), follow these steps:
1. Understand the given values:
- Volume of ethane gas at STP: 64.28 liters
- Molar volume of any ideal gas at STP: 22.4 liters/mole
- Avogadro's number (which is the number of molecules per mole): \(6.022 \times 10^{23} \text{ molecules/mole}\)
2. Calculate the number of moles of ethane gas:
[tex]\[ \text{Number of moles} = \frac{\text{Volume of gas}}{\text{Molar volume at STP}} \][/tex]
Plugging in the values:
[tex]\[ \text{Number of moles} = \frac{64.28 \text{ liters}}{22.4 \text{ liters/mole}} \][/tex]
[tex]\[ \text{Number of moles} \approx 2.8696 \text{ moles} \][/tex]
3. Calculate the number of molecules of ethane:
[tex]\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \][/tex]
Using the calculated number of moles:
[tex]\[ \text{Number of molecules} \approx 2.8696 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \][/tex]
[tex]\[ \text{Number of molecules} \approx 1.7281 \times 10^{24} \text{ molecules} \][/tex]
4. Selecting the answer:
The calculated number of molecules of ethane is approximately \(1.7281 \times 10^{24}\). Among the given choices, the option closest to this value is:
[tex]\[ \boxed{1.728 \times 10^{24}} \][/tex]
Therefore, the correct answer is:
C. [tex]$1.728 \times 10^{24}$[/tex]
1. Understand the given values:
- Volume of ethane gas at STP: 64.28 liters
- Molar volume of any ideal gas at STP: 22.4 liters/mole
- Avogadro's number (which is the number of molecules per mole): \(6.022 \times 10^{23} \text{ molecules/mole}\)
2. Calculate the number of moles of ethane gas:
[tex]\[ \text{Number of moles} = \frac{\text{Volume of gas}}{\text{Molar volume at STP}} \][/tex]
Plugging in the values:
[tex]\[ \text{Number of moles} = \frac{64.28 \text{ liters}}{22.4 \text{ liters/mole}} \][/tex]
[tex]\[ \text{Number of moles} \approx 2.8696 \text{ moles} \][/tex]
3. Calculate the number of molecules of ethane:
[tex]\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \][/tex]
Using the calculated number of moles:
[tex]\[ \text{Number of molecules} \approx 2.8696 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \][/tex]
[tex]\[ \text{Number of molecules} \approx 1.7281 \times 10^{24} \text{ molecules} \][/tex]
4. Selecting the answer:
The calculated number of molecules of ethane is approximately \(1.7281 \times 10^{24}\). Among the given choices, the option closest to this value is:
[tex]\[ \boxed{1.728 \times 10^{24}} \][/tex]
Therefore, the correct answer is:
C. [tex]$1.728 \times 10^{24}$[/tex]
