Given the following reaction:
TiCl4 + O2→ TiO2 + Cl2
If 51.44 g TiCl4 react with 82.32 g O2 complete a mass balance table for this reaction.
To complete a mass balance table for the given reaction, we need to consider the law of conservation of mass. According to this law, the total mass of the reactants must be equal to the total mass of the products.
First, we need to determine the molar masses of each chemical:
- TiCl4 (Titanium(IV) chloride) has a molar mass of (47.867 + 4 x 35.453) g/mol = 189.68 g/mol.
- O2 (oxygen gas) has a molar mass of (2 x 15.999) g/mol = 31.998 g/mol.
- TiO2 (titanium dioxide) has a molar mass of (47.867 + 2 x 15.999) g/mol = 79.866 g/mol.
- Cl2 (chlorine gas) has a molar mass of 2 x 35.453 g/mol = 70.906 g/mol.
Now, let's complete the mass balance table:
| | TiCl4 | O2 | TiO2 | Cl2 |
|------|----------|----------|------------|-----------|
| Mass | 51.44 g | 82.32 g | ??? g | ??? g |
| Moles| 51.44 g (189.68 g/mol) | 82.32 g (31.998 g/mol) | ??? mol (79.866 g/mol) | ??? mol (70.906 g/mol) |
To find the masses of TiO2 and Cl2, we need to determine the number of moles of each compound using the given mass and molar mass.
For TiCl4:
Moles of TiCl4 = mass of TiCl4 / molar mass of TiCl4
= 51.44 g / 189.68 g/mol
≈ 0.271 mol
For O2:
Moles of O2 = mass of O2 / molar mass of O2
= 82.32 g / 31.998 g/mol
≈ 2.572 mol
Now, we can use stoichiometry to relate the moles of the reactants to the moles of products.
From the balanced equation, we can see that the ratio of TiCl4 to TiO2 is 1:1 and the ratio of TiCl4 to Cl2 is also 1:1.
Therefore, the moles of TiO2 and Cl2 will also be 0.271 mol.
Finally, we can determine the masses of TiO2 and Cl2:
Mass of TiO2 = moles of TiO2 x molar mass of TiO2
= 0.271 mol x 79.866 g/mol
≈ 21.66 g
Mass of Cl2 = moles of Cl2 x molar mass of Cl2
= 0.271 mol x 70.906 g/mol
≈ 19.22 g
Now the mass balance table is complete:
| | TiCl4 | O2 | TiO2 | Cl2 |
|------|----------|----------|------------|-----------|
| Mass | 51.44 g | 82.32 g | 21.66 g | 19.22 g |
| Moles| 0.271 mol| 2.572 mol| 0.271 mol | 0.271 mol |
To complete a mass balance table for the given reaction, we need to calculate the masses of all reactants and products involved.
1. Write down the given reaction:
TiCl4 + O2 → TiO2 + Cl2
2. Determine the molar masses of the substances involved:
TiCl4: 4(47.867) + 35.453 = 189.68 g/mol
O2: 2(15.999) = 31.998 g/mol
TiO2: 47.867 + 2(15.999) = 79.866 g/mol
Cl2: 2(35.453) = 70.906 g/mol
3. Calculate the number of moles for each reactant and product using the given masses:
Moles of TiCl4: 51.44 g / 189.68 g/mol = 0.2710 mol
Moles of O2: 82.32 g / 31.998 g/mol = 2.573 mol
4. Determine the stoichiometry ratios based on the balanced equation:
For TiCl4, the stoichiometry ratio is 1:0 (reactant)
For O2, the stoichiometry ratio is 1:1 (reactant)
For TiO2, the stoichiometry ratio is 1:1 (product)
For Cl2, the stoichiometry ratio is 1:1 (product)
5. Calculate the masses of TiO2 and Cl2 produced using stoichiometry ratios:
Mass of TiO2 = Moles of TiO2 × Molar mass of TiO2
= 0.2710 mol × 79.866 g/mol
= 21.658 g
Mass of Cl2 = Moles of Cl2 × Molar mass of Cl2
= 0.2710 mol × 70.906 g/mol
= 19.211 g
6. Complete the mass balance table:
| Substance | Initial Mass (g) | Moles | Stoichiometry | Final Mass (g) |
|-----------|-----------------|-------|---------------|----------------|
| TiCl4 | 51.44 | 0.271 | 1:0 | 0.000 |
| O2 | 82.32 | 2.573 | 1:1 | 2.573 |
| TiO2 | 0.000 | 0.271 | 1:1 | 21.658 |
| Cl2 | 0.000 | 0.271 | 1:1 | 19.211 |
Therefore, based on the mass balance table, 51.44 g of TiCl4 and 82.32 g of O2 will produce 21.658 g of TiO2 and 19.211 g of Cl2 in the reaction.