How many C2H4 molecules are in 45.8 g of C2H4? The molar mass of C2H4 is 28.05 g/mol. Group of answer choices 3.69 x 1023 C2H4 molecules 9.83 x 1023 C2H4 molecules 4.69 x 1026 C2H4 molecules 2.71 x 1023 C2H4 molecules 7.74 x 1026 C2H4 molecules
The Correct Answer and Explanation is:
To find how many C₂H₄ molecules are in 45.8 grams of C₂H₄, we use the following steps:
Step 1: Use the molar mass to find moles
Given:
- Mass of ethene (C₂H₄) = 45.8 grams
- Molar mass of C₂H₄ = 28.05 g/mol
Moles of C₂H₄ =massmolar mass=45.8 g28.05 g/mol≈1.633 mol\frac{\text{mass}}{\text{molar mass}} = \frac{45.8\ \text{g}}{28.05\ \text{g/mol}} \approx 1.633\ \text{mol}molar massmass=28.05 g/mol45.8 g≈1.633 mol
Step 2: Use Avogadro’s number to convert moles to molecules
Avogadro’s number is6.022×1023 molecules/mol6.022 \times 10^{23}\ \text{molecules/mol}6.022×1023 molecules/mol
So the number of molecules is1.633 mol×6.022×1023 molecules/mol≈9.83×1023 molecules1.633\ \text{mol} \times 6.022 \times 10^{23}\ \text{molecules/mol} \approx 9.83 \times 10^{23}\ \text{molecules}1.633 mol×6.022×1023 molecules/mol≈9.83×1023 molecules
Final Answer:
9.83 × 10²³ C₂H₄ molecules
Explanation
To determine the number of ethene molecules in a given mass, we must connect grams to individual particles using two key concepts: molar mass and Avogadro’s number. The molar mass of a compound tells us how many grams are in one mole of that substance. For ethene, or C₂H₄, the molar mass is 28.05 grams per mole. This means one mole of ethene weighs 28.05 grams and contains exactly 6.022 × 10²³ molecules, which is Avogadro’s constant.
We start by converting grams into moles. This is done by dividing the mass of the sample by its molar mass. For 45.8 grams of ethene, we divide by 28.05 g/mol, giving approximately 1.633 moles. Each mole represents a very large number of molecules, so we then multiply the number of moles by Avogadro’s number to find the actual count of molecules.
When 1.633 moles are multiplied by 6.022 × 10²³, the result is around 9.83 × 10²³ molecules. This is the total number of ethene molecules in 45.8 grams of the compound.
This process shows how chemical quantities in grams relate to microscopic quantities of particles. It is a fundamental concept in chemistry, helping chemists understand how much of a substance is present at the molecular level, even when working with amounts that are visible and measurable in a laboratory setting.
✅ Correct choice: 9.83 × 10²³ C₂H₄ molecules
