One gram of TNT, C7H5N3O6, has 1.33 ´ 1022 hydrogen atoms. How many carbon atoms are there in 1.00 g of TNT?
There are 7 C atoms for every 5 H atoms; therefore, 1.33 x 10^22 H atoms x (7C/5H) = ??
To find the number of carbon atoms in 1.00 g of TNT (C7H5N3O6), we first need to calculate the molar mass of TNT and then use the Avogadro's number.
Here's how to do it:
Step 1: Calculate the molar mass of TNT (C7H5N3O6)
- Look up the atomic masses of carbon (C), hydrogen (H), nitrogen (N), and oxygen (O).
- Multiply the atomic masses by the number of atoms in each element in the TNT formula.
- Add up the results.
The atomic masses are:
Carbon (C): 12.01 g/mol
Hydrogen (H): 1.01 g/mol
Nitrogen (N): 14.01 g/mol
Oxygen (O): 16.00 g/mol
Calculating the molar mass:
Molar mass of C7H5N3O6 = (7 * 12.01 g/mol) + (5 * 1.01 g/mol) + (3 * 14.01 g/mol) + (6 * 16.00 g/mol)
= 84.07 g/mol + 5.05 g/mol + 42.03 g/mol + 96.00 g/mol
= 227.15 g/mol
Therefore, the molar mass of TNT is 227.15 g/mol.
Step 2: Determine the number of moles of TNT in 1.00 g
- Use the formula: Moles = Mass / Molar mass
- Substitute the given values: Moles of TNT = 1.00 g / 227.15 g/mol
- Calculate the result: Moles of TNT = 0.00439 mol
Step 3: Use Avogadro's number to find the number of carbon atoms
- Avogadro's number states that there are 6.022 x 10^23 atoms in one mole of any substance.
- Multiply the number of moles of TNT by Avogadro's number to find the number of carbon atoms.
Number of carbon atoms = Moles of TNT * Avogadro's number
= 0.00439 mol * 6.022 x 10^23 atoms/mol
Calculating the result:
Number of carbon atoms = 2.6478 x 10^21 carbon atoms
Therefore, there are approximately 2.65 x 10^21 carbon atoms in 1.00 g of TNT.