How many C2H 4 molecules are contained in 45.8 mg of C2H 4? The molar mass of C2H 4 is 28.05 g/mol.
7.74 x 1026 C2H4 molecules
4.69 x 1023 C2H4 molecules
3.69 x 1023 C2H4 molecules
9.83 x 1020 C2H4 molecules
% 1020 C2H4 molecules
The Correct Answer and Explanation is :
To determine how many molecules of C₂H₄ (ethylene) are contained in 45.8 mg of C₂H₄, we need to go through the following steps:
Step 1: Convert mass to grams
We are given 45.8 mg of C₂H₄, but we need the mass in grams. Since there are 1000 mg in 1 g:
[
45.8 \, \text{mg} = \frac{45.8}{1000} \, \text{g} = 0.0458 \, \text{g}
]
Step 2: Calculate the number of moles of C₂H₄
Next, we use the molar mass of C₂H₄ to convert the mass into moles. The molar mass of C₂H₄ is given as 28.05 g/mol. The number of moles (n) can be calculated using the formula:
[
n = \frac{\text{mass}}{\text{molar mass}}
]
Substituting the known values:
[
n = \frac{0.0458 \, \text{g}}{28.05 \, \text{g/mol}} = 0.001634 \, \text{mol}
]
Step 3: Calculate the number of molecules
To calculate the number of molecules, we use Avogadro’s number, which is (6.022 \times 10^{23}) molecules per mole. The number of molecules is:
[
\text{Number of molecules} = n \times N_A
]
Where (N_A) is Avogadro’s number. Substituting the values:
[
\text{Number of molecules} = 0.001634 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
]
[
\text{Number of molecules} = 9.83 \times 10^{20} \, \text{molecules}
]
Conclusion:
The correct answer is 9.83 × 10²⁰ molecules of C₂H₄.
Explanation:
In this problem, we used basic stoichiometric conversions. First, we converted the given mass to grams, then used the molar mass of C₂H₄ to find the number of moles. Finally, we multiplied by Avogadro’s number to find the number of molecules. This is a standard process in chemistry to determine the number of molecules or atoms in a given sample.