How many grams of sodium carbonate are in a sodium carbonate sample that contains 1.773x10^17 carbon atoms? How do I work this out?
There are 6.022E23 C atoms in a mole of C and there is just 1 C atom in Na2CO3 molecule.
You have 1.773E17 C atoms which must mean 1.773E17 Na2CO3 molecules so that is
1.77E17/6.022E23 = estimated 3E-7 mols.
Convert that to grams; g = mols x molar mass = ?
To determine the number of grams of sodium carbonate in a sample containing a given number of carbon atoms, you need to follow a series of steps. Here's how you can work it out:
Step 1: Find the molar mass of sodium carbonate.
The molar mass of sodium carbonate (Na2CO3) can be calculated by adding up the atomic masses of each individual element in the compound. Using the periodic table, you can find the atomic masses of sodium (Na), carbon (C), and oxygen (O). The atomic masses are approximately 22.99 g/mol for Na, 12.01 g/mol for C, and 16.00 g/mol for O. The molar mass of Na2CO3 is then calculated as follows:
Molar mass of Na2CO3 = (2 * Na) + C + (3 * O)
= (2 * 22.99 g/mol) + 12.01 g/mol + (3 * 16.00 g/mol)
= 105.99 g/mol + 12.01 g/mol + 48.00 g/mol
= 166.00 g/mol
Step 2: Calculate the number of moles of carbon atoms.
You need to convert the given number of carbon atoms (1.773x10^17) into moles. Use Avogadro's number, which states that 1 mole of any substance contains 6.022x10^23 particles (atoms, molecules, etc.). The conversion is as follows:
Number of moles of carbon atoms = (Given number of carbon atoms) / Avogadro's number
= (1.773x10^17) / (6.022x10^23)
≈ 2.94x10^-7 moles (approximately)
Step 3: Convert moles of carbon atoms to moles of sodium carbonate.
The ratio between the carbon atoms and the sodium carbonate molecules is 1:1. Therefore, the number of moles of carbon atoms is equal to the number of moles of sodium carbonate.
Moles of sodium carbonate = Moles of carbon atoms
≈ 2.94x10^-7 moles
Step 4: Convert moles of sodium carbonate to grams.
Multiply the number of moles of sodium carbonate by its molar mass to obtain the mass in grams.
Mass of sodium carbonate = Moles of sodium carbonate * Molar mass of Na2CO3
= 2.94x10^-7 moles * 166.00 g/mol
≈ 4.87x10^-5 grams (approximately)
Therefore, there are approximately 4.87x10^-5 grams (or 0.0487 milligrams) of sodium carbonate in the given sample containing 1.773x10^17 carbon atoms.
To find the number of grams of sodium carbonate in a sample, you first need to determine the molar mass of sodium carbonate and the number of moles of sodium carbonate in the sample. Then, you can use the relationship between moles and grams to calculate the mass.
Here's how you can work it out step-by-step:
Step 1: Find the molar mass of sodium carbonate (Na2CO3).
The molar mass is the sum of the atomic masses of each element in the compound. The atomic masses are found on the periodic table.
- Sodium (Na) has an atomic mass of 22.99 g/mol.
- Carbon (C) has an atomic mass of 12.01 g/mol.
- Oxygen (O) has an atomic mass of 16.00 g/mol.
The molar mass of Na2CO3 is:
2(Na) + 1(C) + 3(O) = (2 x 22.99 g/mol) + (12.01 g/mol) + (3 x 16.00 g/mol)
= 45.98 g/mol + 12.01 g/mol + 48.00 g/mol
= 105.99 g/mol
Step 2: Calculate the number of moles of sodium carbonate in the sample.
Given the number of carbon atoms (1.773x10^17), you need to convert this into moles.
To do this, you'll use Avogadro's number (6.022 x 10^23) which is the number of atoms in one mole of a substance.
Number of moles of sodium carbonate = (Number of carbon atoms) / (Avogadro's number)
= (1.773x10^17) / (6.022 x 10^23)
Step 3: Calculate the mass of sodium carbonate.
Now that you have the number of moles of sodium carbonate, you can use the molar mass to calculate the mass in grams.
Mass (grams) = (Number of moles of sodium carbonate) x (Molar mass)
= (1.773x10^17) / (6.022 x 10^23) x 105.99 g/mol
By multiplying these values, you will get the grams of sodium carbonate in the sample.
Please perform the calculations for the precise result.