Answer :
Answer: The mass of [tex]AgC_{10}H_9N_4SO_2[/tex] produced is 21.13 grams
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
- For silver (I) oxide:
Given mass of silver (I) oxide = 3.024 g
Molar mass of silver (I) oxide = 102.1 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of silver (I) oxide}=\frac{3.024g}{102.1g/mol}=0.0296mol[/tex]
- For [tex]C_{10}H_{10}N_4SO_2[/tex] :
Given mass of [tex]C_{10}H_{10}N_4SO_2[/tex] = 50.0 g
Molar mass of [tex]C_{10}H_{10}N_4SO_2[/tex] = 250 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of }C_{10}H_{10}N_4SO_2=\frac{50.0g}{250g/mol}=0.2mol[/tex]
The chemical equation for the combustion of hexane follows:
[tex]Ag_2O(s)+2C_{10}H_{10}N_4SO_2(s)\rightarrow 2AgC_{10}H_9N_4SO_2(s)+H_2O(l)[/tex]
By Stoichiometry of the reaction:
1 mole of silver (I) oxide reacts with 2 moles of [tex]C_{10}H_{10}N_4SO_2[/tex]
So, 0.0296 moles of silver (I) oxide will react with = [tex]\frac{2}{1}\times 0.0296=0.0592mol[/tex] of [tex]C_{10}H_{10}N_4SO_2[/tex]
As, given amount of [tex]C_{10}H_{10}N_4SO_2[/tex] is more than the required amount. So, it is considered as an excess reagent.
Thus, silver (I) oxide is considered as a limiting reagent because it limits the formation of product.
By Stoichiometry of the reaction:
1 mole of silver (I) oxide produces 2 moles of [tex]AgC_{10}H_9N_4SO_2[/tex]
So, 0.0296 moles of silver (I) oxide will produce = [tex]\frac{2}{1}\times 0.0296=0.0592moles[/tex] of [tex]AgC_{10}H_9N_4SO_2[/tex]
Now, calculating the mass of [tex]AgC_{10}H_9N_4SO_2[/tex] from equation 1, we get:
Molar mass of [tex]AgC_{10}H_9N_4SO_2[/tex] = 357 g/mol
Moles of [tex]AgC_{10}H_9N_4SO_2[/tex] = 0.0592 moles
Putting values in equation 1, we get:
[tex]0.0592mol=\frac{\text{Mass of }AgC_{10}H_9N_4SO_2}{357g/mol}\\\\\text{Mass of }AgC_{10}H_9N_4SO_2=(0.0592mol\times 357g/mol)=21.13g[/tex]
Hence, the mass of [tex]AgC_{10}H_9N_4SO_2[/tex] produced is 21.13 grams