Determine the quantity of nitrogen atoms in 15.0 grams of Pb(NO2)2
The Correct Answer and Explanation is:
To determine the quantity of nitrogen atoms in 15.0 grams of Pb(NO2)2, we need to follow a step-by-step process:
Step 1: Calculate the molar mass of Pb(NO2)2.
We begin by finding the molar mass of the compound, Pb(NO2)2, by adding the atomic masses of each element in the formula.
- Lead (Pb): 207.2 g/mol
- Nitrogen (N): 14.0 g/mol
- Oxygen (O): 16.0 g/mol
The formula, Pb(NO2)2, indicates that there is one Pb atom, two nitrogen atoms, and four oxygen atoms.
So, the molar mass of Pb(NO2)2 is calculated as:Molar mass of Pb(NO2)2=207.2 g/mol+2×(14.0 g/mol)+4×(16.0 g/mol)\text{Molar mass of Pb(NO2)2} = 207.2 \, \text{g/mol} + 2 \times (14.0 \, \text{g/mol}) + 4 \times (16.0 \, \text{g/mol})Molar mass of Pb(NO2)2=207.2g/mol+2×(14.0g/mol)+4×(16.0g/mol)=207.2+28.0+64.0=299.2 g/mol= 207.2 + 28.0 + 64.0 = 299.2 \, \text{g/mol}=207.2+28.0+64.0=299.2g/mol
Step 2: Calculate the number of moles of Pb(NO2)2.
Next, we calculate the number of moles of Pb(NO2)2 in 15.0 grams using the formula:moles of Pb(NO2)2=mass of Pb(NO2)2molar mass of Pb(NO2)2=15.0 g299.2 g/mol=0.0501 mol\text{moles of Pb(NO2)2} = \frac{\text{mass of Pb(NO2)2}}{\text{molar mass of Pb(NO2)2}} = \frac{15.0 \, \text{g}}{299.2 \, \text{g/mol}} = 0.0501 \, \text{mol}moles of Pb(NO2)2=molar mass of Pb(NO2)2mass of Pb(NO2)2=299.2g/mol15.0g=0.0501mol
Step 3: Determine the number of nitrogen atoms.
Since each molecule of Pb(NO2)2 contains 2 nitrogen atoms, the number of nitrogen atoms is twice the number of moles of Pb(NO2)2. We multiply the moles of Pb(NO2)2 by 2 to find the number of moles of nitrogen atoms:moles of nitrogen atoms=0.0501 mol×2=0.1002 mol\text{moles of nitrogen atoms} = 0.0501 \, \text{mol} \times 2 = 0.1002 \, \text{mol}moles of nitrogen atoms=0.0501mol×2=0.1002mol
Finally, to determine the number of nitrogen atoms, we multiply the moles of nitrogen atoms by Avogadro’s number (6.022 × 10²³ atoms/mol):number of nitrogen atoms=0.1002 mol×6.022×1023 atoms/mol=6.03×1022 atoms\text{number of nitrogen atoms} = 0.1002 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.03 \times 10^{22} \, \text{atoms}number of nitrogen atoms=0.1002mol×6.022×1023atoms/mol=6.03×1022atoms
Final Answer:
The quantity of nitrogen atoms in 15.0 grams of Pb(NO2)2 is 6.03 × 10²² atoms.
