Respuesta :
Answer: The mass of MgO formed is 3.502 grams and mass of [tex]Mg_3N_2[/tex] formed is 1.587 grams.
Explanation:
We are given:
Total mass of magnesium reacted = 3.26 g
Total mass of products formed = 5.09 g
To calculate number of moles of a substance, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
- For calculating mass of MgO:
The chemical equation for the formation of magnesium oxide follows:
[tex]2Mg+O_2\rightarrow 2MgO[/tex]
Let 'x' grams of magnesium is reacting to form magnesium oxide.
Molar mass of Magnesium = 24.3 g/mol
Putting values in equation 1, we get:
Number of moles of magnesium = [tex]\frac{x}{24.3}mol[/tex]
By Stoichiometry of the reaction:
2 moles of magnesium produces 2 moles of MgO
So, [tex]\frac{x}{24.3}[/tex] moles of magnesium will produce [tex]\frac{2}{2}\times \frac{x}{24.3}=\frac{x}{24.3}[/tex] moles of MgO
Molar mass of MgO = 40.3 g/mol
Putting values in equation 1, we get:
Mass of MgO = [tex]\frac{x}{24.3}\times 40.3=(1.66\times x)g[/tex]
Mass of magnesium oxide = [tex](1.66\times x)g[/tex] = X grams
- For calculating mass of [tex]Mg_3N_2[/tex] :
The chemical equation for the formation of magnesium nitride follows:
[tex]3Mg+N_2\rightarrow Mg_3N_2[/tex]
Mass of magnesium reacting = (3.26 - x)
Molar mass of Magnesium = 24.3 g/mol
Putting values in equation 1, we get:
Number of moles of magnesium = [tex]\frac{(3.26-x)}{24.3}mol[/tex]
By Stoichiometry of the reaction:
3 moles of magnesium produces 1 moles of [tex]Mg_3N_2[/tex]
So, [tex]\frac{(3.26-x)}{24.3}[/tex] moles of magnesium will produce [tex]\frac{1}{3}\times \frac{(3.26-x)}{24.3}=\frac{(3.26-x)}{72.9}[/tex] moles of [tex]Mg_3N_2[/tex]
Molar mass of [tex]Mg_3N_2[/tex] = 101 g/mol
Putting values in equation 1, we get:
Mass of [tex]Mg_3N_2=\frac{(3.26-x)}{72.9}\times 101=[(3.26-x)\times 1.38]g[/tex]
Mass of magnesium nitride = [tex][(3.26-x)\times 1.38]g[/tex] = Y grams
- Calculating the mass of products:
Total mass of the products = 5.09 grams
[tex]X+Y=5.09[/tex]
Putting values of 'X' and 'Y' in above equation, we get:
[tex](1.66\times x)+[(3.26-x)\times 1.38]=5.09\\\\x=2.11g[/tex]
Mass of MgO = [tex](1.66\times 2.11)=3.502g[/tex]
Mass of [tex]Mg_3N_2=[(3.26-2.11)\times 1.38]=1.587g[/tex]
Hence, the mass of MgO formed is 3.502 grams and mass of [tex]Mg_3N_2[/tex] formed is 1.587 grams.
