Question
A molecule of oxygen, O,2, weights 32 amu (16 amu per oxygen atom). A molecule of water, H2O, weighs 18 amu, If 320 amu of O2 arn 540 amu of rH2O react with the varnish, how many molecules of varnish were modified as the painting aged
Answers
GPT-4o mini
To find out how many molecules of varnish were modified as the painting aged, we first need to calculate the moles of O₂ and H₂O that reacted, then determine how many molecules correspond to those moles.
1. **Calculate moles of O₂:**
- We know that the molar mass of O₂ is 32 amu, or 32 g/mol.
- To find the number of moles in 320 amu of O₂, we use the formula:
\[
\text{moles of O₂} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{320 \text{ amu}}{32 \text{ g/mol}} = 10 \text{ moles of O₂}
\]
2. **Calculate moles of H₂O:**
- The molar mass of H₂O is 18 amu, or 18 g/mol.
- To find the number of moles in 540 amu of H₂O:
\[
\text{moles of H₂O} = \frac{540 \text{ amu}}{18 \text{ g/mol}} = 30 \text{ moles of H₂O}
\]
3. **Determine the reactions:**
- The stoichiometry of the reaction between O₂ and H₂O, and how these react with varnish, is not specified in your question. However, if we assume a proportionate relationship, we need to know how many molecules of varnish are modified per mole of O₂ and H₂O.
4. **Convert moles to molecules:**
- Now we can calculate the total number of molecules involved. Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole:
- For O₂:
\[
\text{molecules of O₂} = 10 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \approx 6.022 \times 10^{24} \text{ molecules of O₂}
\]
- For H₂O:
\[
\text{molecules of H₂O} = 30 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \approx 1.8066 \times 10^{25} \text{ molecules of H₂O}
\]
5. **Determine total modified varnish molecules:**
- We need additional information on the reaction stoichiometry to determine how many molecules of varnish were modified. If it takes a specific number of molecules of O₂ and H₂O to modify one molecule of varnish, then we could determine the total number modified.
- For example, if we assume that the ratio is 1:1 (one molecule of O₂ and one molecule of H₂O modifies one molecule of varnish), then you would take the lesser of the two, which would be 10 moles of O₂ (thus, 10 moles of varnish).
If you can provide the specific stoichiometric relationship between O₂, H₂O, and the varnish, we can better calculate the total molecules of varnish affected through the reactions. Without this, the above calculations lead us to a theoretical approach rather than an exact number of modified varnish molecules.
1. **Calculate moles of O₂:**
- We know that the molar mass of O₂ is 32 amu, or 32 g/mol.
- To find the number of moles in 320 amu of O₂, we use the formula:
\[
\text{moles of O₂} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{320 \text{ amu}}{32 \text{ g/mol}} = 10 \text{ moles of O₂}
\]
2. **Calculate moles of H₂O:**
- The molar mass of H₂O is 18 amu, or 18 g/mol.
- To find the number of moles in 540 amu of H₂O:
\[
\text{moles of H₂O} = \frac{540 \text{ amu}}{18 \text{ g/mol}} = 30 \text{ moles of H₂O}
\]
3. **Determine the reactions:**
- The stoichiometry of the reaction between O₂ and H₂O, and how these react with varnish, is not specified in your question. However, if we assume a proportionate relationship, we need to know how many molecules of varnish are modified per mole of O₂ and H₂O.
4. **Convert moles to molecules:**
- Now we can calculate the total number of molecules involved. Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole:
- For O₂:
\[
\text{molecules of O₂} = 10 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \approx 6.022 \times 10^{24} \text{ molecules of O₂}
\]
- For H₂O:
\[
\text{molecules of H₂O} = 30 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \approx 1.8066 \times 10^{25} \text{ molecules of H₂O}
\]
5. **Determine total modified varnish molecules:**
- We need additional information on the reaction stoichiometry to determine how many molecules of varnish were modified. If it takes a specific number of molecules of O₂ and H₂O to modify one molecule of varnish, then we could determine the total number modified.
- For example, if we assume that the ratio is 1:1 (one molecule of O₂ and one molecule of H₂O modifies one molecule of varnish), then you would take the lesser of the two, which would be 10 moles of O₂ (thus, 10 moles of varnish).
If you can provide the specific stoichiometric relationship between O₂, H₂O, and the varnish, we can better calculate the total molecules of varnish affected through the reactions. Without this, the above calculations lead us to a theoretical approach rather than an exact number of modified varnish molecules.