A mixture contains 0.218 mol of Mn2O3 and 17.8 g of MnO2.
1.How many atoms of oxygen are present in the mixture?
2.How many grams of manganese are in the mixture?
molecules Mn2O3 = mols x 6.02E23 = ?
molecules O in Mn2O3 = 3x that
mols MnO2 = grams/molar mass = ?
molecules MnO2 = mols x 6.023E23 =?
molecules O atoms is 2x that.
Total O atoms = sum of the two.
2 is worked the same way.
To solve these problems, we will use the mole concept to convert between moles and atoms, and between moles and grams.
1. How many atoms of oxygen are present in the mixture?
- First, we need to find the number of moles of oxygen in each compound.
- For Mn2O3:
The molar mass of Mn2O3 is calculated as:
(2 * atomic mass of Mn) + (3 * atomic mass of O)
= (2 * 54.938045 g/mol) + (3 * 15.999 g/mol)
= 109.87609 g/mol + 47.997 g/mol
= 157.87309 g/mol
Now, we can calculate the number of moles of oxygen in Mn2O3 using the given number of moles:
moles of O in Mn2O3 = (0.218 mol) * (3 mol O / 1 mol Mn2O3)
= 0.218 mol * 3 mol O / 1 mol Mn2O3
= 0.654 mol O
- For MnO2:
The molar mass of MnO2 is calculated as:
atomic mass of Mn + (2 * atomic mass of O)
= 54.938045 g/mol + (2 * 15.999 g/mol)
= 54.938045 g/mol + 31.998 g/mol
= 86.936045 g/mol
Now, we can calculate the number of moles of oxygen in MnO2 using the given mass:
moles of O in MnO2 = (17.8 g) * (1 mol O / 86.936045 g MnO2)
= 17.8 g * 1 mol O / 86.936045 g MnO2
= 0.204 mol O
- Finally, we can calculate the total number of moles of oxygen in the mixture by adding the moles of oxygen from both compounds:
total moles of O = moles of O in Mn2O3 + moles of O in MnO2
= 0.654 mol + 0.204 mol
= 0.858 mol
- Since 1 mole contains 6.022 x 10^23 atoms (Avogadro's number), we can calculate the number of atoms of oxygen in the mixture:
number of atoms of O = total moles of O * Avogadro's number
= 0.858 mol * 6.022 x 10^23 atoms/mol
= 5.17 x 10^23 atoms of oxygen
Therefore, there are approximately 5.17 x 10^23 atoms of oxygen present in the mixture.
2. How many grams of manganese are in the mixture?
- First, we need to find the number of moles of manganese in each compound.
- For Mn2O3:
The molar mass of Mn2O3 is calculated as:
(2 * atomic mass of Mn) + (3 * atomic mass of O)
= (2 * 54.938045 g/mol) + (3 * 15.999 g/mol)
= 109.87609 g/mol + 47.997 g/mol
= 157.87309 g/mol
Now, we can calculate the number of moles of manganese in Mn2O3 using the given number of moles:
moles of Mn in Mn2O3 = (0.218 mol) * (2 mol Mn / 1 mol Mn2O3)
= 0.218 mol * 2 mol Mn / 1 mol Mn2O3
= 0.436 mol Mn
- For MnO2:
The molar mass of MnO2 is calculated as:
atomic mass of Mn + (2 * atomic mass of O)
= 54.938045 g/mol + (2 * 15.999 g/mol)
= 54.938045 g/mol + 31.998 g/mol
= 86.936045 g/mol
Now, we can calculate the number of moles of manganese in MnO2 using the given mass:
moles of Mn in MnO2 = (17.8 g) * (1 mol Mn / 86.936045 g MnO2)
= 17.8 g * 1 mol Mn / 86.936045 g MnO2
= 0.205 mol Mn
- Finally, we can calculate the total number of moles of manganese in the mixture by adding the moles of manganese from both compounds:
total moles of Mn = moles of Mn in Mn2O3 + moles of Mn in MnO2
= 0.436 mol + 0.205 mol
= 0.641 mol
- We can now calculate the mass of manganese in the mixture using the molar mass of manganese:
mass of Mn = total moles of Mn * molar mass of Mn
= 0.641 mol * 54.938045 g/mol
= 35.307 g
Therefore, there are approximately 35.307 grams of manganese in the mixture.
To solve these problems, let's start by determining the number of moles of MnO2.
1. Calculate the number of moles of MnO2:
To do this, we'll use the molar mass of MnO2, which is 86.94 g/mol. We can use this formula:
Moles = Mass / Molar Mass
Moles of MnO2 = 17.8 g / 86.94 g/mol = 0.205 mol
Now, let's determine the number of moles of oxygen in MnO2 and Mn2O3.
1. Moles of oxygen in MnO2:
For every 1 mole of MnO2, there are 2 moles of oxygen. So, the number of moles of oxygen in MnO2 is:
Moles of oxygen = Moles of MnO2 x 2 = 0.205 mol x 2 = 0.41 mol
2. Moles of oxygen in Mn2O3:
For every 1 mole of Mn2O3, there are 3 moles of oxygen. To find the moles of oxygen in Mn2O3, we need to convert the moles of Mn2O3 to moles of oxygen. Since we have 0.218 moles of Mn2O3:
Moles of oxygen = Moles of Mn2O3 x 3 = 0.218 mol x 3 = 0.654 mol
Now, let's find the total moles of oxygen in the mixture:
Total moles of oxygen = Moles of oxygen in MnO2 + Moles of oxygen in Mn2O3 = 0.41 mol + 0.654 mol = 1.064 mol
The total number of atoms of oxygen can be calculated by multiplying the total moles of oxygen by Avogadro's number, which is 6.022 x 10^23.
Total atoms of oxygen = Total moles of oxygen x Avogadro's number = 1.064 mol x 6.022 x 10^23 atoms/mol
2. Now let's find the grams of manganese in the mixture:
To determine the grams of manganese, we need to add the grams of MnO2 (given) and Mn2O3 (which we can calculate).
1. Given: Mass of MnO2 = 17.8 grams
2. Moles of Mn2O3 = 0.218 moles (given)
3. Molar mass of Mn2O3 = (Molar mass of Mn x 2) + (Molar mass of O x 3) = (55.85 g/mol x 2) + (16 g/mol x 3) = 111.7 g/mol + 48 g/mol = 159.7 g/mol
Now we can determine the grams of Mn2O3:
Grams of Mn2O3 = Moles of Mn2O3 x Molar mass of Mn2O3 = 0.218 mol x 159.7 g/mol
Finally, we can calculate the grams of manganese in the mixture:
Grams of manganese = Grams of MnO2 + Grams of Mn2O3 = 17.8 g + (0.218 mol x 159.7 g/mol)