calculate the mass of 2*10power 10 molecules of nitrogen gas
The correct answer and explanation is:
To calculate the mass of 2×10102 \times 10^{10} molecules of nitrogen gas (N₂), we will use the following steps:
✅ Step 1: Use Avogadro’s Number
Avogadro’s number tells us how many molecules are in 1 mole of any substance: NA=6.022×1023 molecules/molN_A = 6.022 \times 10^{23} \text{ molecules/mol}
✅ Step 2: Find the Molar Mass of N₂
The atomic mass of nitrogen (N) is approximately 14.01 g/mol, so: Molar mass of N2=2×14.01=28.02 g/mol\text{Molar mass of N}_2 = 2 \times 14.01 = 28.02 \text{ g/mol}
✅ Step 3: Convert Molecules to Moles
We are given: Number of molecules=2×1010\text{Number of molecules} = 2 \times 10^{10}
To find the number of moles, divide the number of molecules by Avogadro’s number: Moles=2×10106.022×1023≈3.32×10−14 mol\text{Moles} = \frac{2 \times 10^{10}}{6.022 \times 10^{23}} \approx 3.32 \times 10^{-14} \text{ mol}
✅ Step 4: Calculate the Mass
Now, multiply the number of moles by the molar mass: Mass=moles×molar mass\text{Mass} = \text{moles} \times \text{molar mass} Mass=(3.32×10−14)×28.02≈9.3×10−13 g\text{Mass} = (3.32 \times 10^{-14}) \times 28.02 \approx 9.3 \times 10^{-13} \text{ g}
✅ Final Answer:
9.3×10−13 grams\boxed{9.3 \times 10^{-13} \text{ grams}}
🧠 Explanation (300 words)
To determine the mass of a specific number of nitrogen gas molecules, we need to connect microscopic particles (molecules) to macroscopic units (grams). This is made possible by Avogadro’s number, which relates the number of particles in a mole—one of the fundamental units in chemistry.
Avogadro’s number, 6.022×10236.022 \times 10^{23}, indicates that a mole contains that many molecules. If we are given a much smaller number of molecules, like 2×10102 \times 10^{10}, we first convert this to moles by dividing it by Avogadro’s number. This gives us a very tiny number of moles (3.32×10−143.32 \times 10^{-14}), since 2×10102 \times 10^{10} molecules is just a minuscule fraction of a mole.
Next, we use the molar mass of nitrogen gas (N₂), which is about 28.02 g/mol. This value tells us the mass of one mole of nitrogen gas. By multiplying our small number of moles by this molar mass, we find the actual mass of our sample.
In this case, the final answer is approximately 9.3×10−139.3 \times 10^{-13} grams—an extremely small quantity, which makes sense given the very small number of molecules. This type of calculation is foundational in chemistry, especially when working with molecular scales in areas such as stoichiometry, gas laws, or molecular biology.