Respuesta :
Answer: The enthalpy of the reaction is [tex]5.30\times 10^{-4}kJ[/tex]
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 metal:
Given mass of metal = 0.295 g
Molar mass of metal = 57.78 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of metal}=\frac{0.295g}{57.78g/mol}=0.0051mol[/tex]
- To calculate the moles of a solute, we use the equation:
[tex]\text{Molarity of the solution}=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}[/tex]
We are given:
Volume of hydrochloric acid = 65 mL = 0.065 L (Conversion factor: 1 L = 1000 mL)
Molarity of the solution = 1 moles/ L
Putting values in above equation, we get:
[tex]1mol/L=\frac{\text{Moles of hydrochloric acid}}{0.065L}\\\\\text{Moles of hydrochloric acid}=0.065mol[/tex]
- For the given chemical reaction:
[tex]M(s)+2HCl(aq.)\rightarrow MCl_2(aq.)+H_2(g)[/tex]
By Stoichiometry of the reaction:
1 mole of metal reacts with 2 moles of hydrochloric acid..
So, 0.0051 moles of metal will react with = [tex]\frac{2}{1}\times 0.0051=0.0102moles[/tex] of hydrochloric acid.
As, given amount of hydrochloric acid is more than the required amount. So, it is considered as an excess reagent.
Thus, metal is considered as a limiting reagent because it limits the formation of product.
By Stoichiometry of the reaction:
If 1 mole of metal absorbs 104 J of heat
Then, 0.0051 moles of metal will absorb = [tex]\frac{104J}{1mol}\times 0.0051mol=0.530J[/tex] of heat.
Converting joules to kilo joules, we use the conversion factor:
[tex]1kJ=1000J[/tex]
Converting the given value in kilo joules, we get:
[tex]\Rightarrow \frac{0.530J}{1000J}\times 1kJ=5.30\times 10^{-4}kJ[/tex]
Hence, the enthalpy of the reaction is [tex]5.30\times 10^{-4}kJ[/tex]
Enthalpy is the total internal energy of the system and the product of the system's pressure and volume. The enthalpy of the reaction is [tex]5.30\times 10^{-4} \;\rm kJ.[/tex]
What is enthalpy?
Enthalpy of the reaction is estimated at constant pressure and gives the amount of heat. It can be used to measure chemical or biological reactions.
Given,
- The volume of hydrochloric acid = 65 mL
- Molarity of the solution = 1 moles/ L
- Mass of metal = 0.295 g
- Molar mass of metal = 57.78 g/mol
First, calculate the number of moles of metal:
[tex]\begin{aligned}\rm Moles (n) &= \dfrac{\rm mass}{\rm molar \;mass}\\\\\rm n &= \dfrac{0.295}{57.78}\\\\&= 0.0051 \;\rm moles \end{aligned}[/tex]
Second, calculate the moles of HCl:
[tex]\begin{aligned}\rm Molarity (M) &= \dfrac{\rm moles (n)}{0.065\;\rm L}\\\\&= 0.065 \rm\;moles\end{aligned}[/tex]
From the chemical reaction in the question, the stoichiometry is,
1 mole of metal reacts with 2 moles of HCl.
So, 0.0051 moles of metal = X moles of HCl
Solving of for X = 0.0102 moles
From this, it can be inferred that the Hydrochloric acid is in excess amount and the metal is the limiting reagent.
From the reaction,
1 mole of metal absorbs heat = 104 J
0.0051 moles of metal absorbs heat = ?
Solving further,
[tex]\begin{aligned}&=\dfrac{104 \;\rm J \times 0.0051 \;\rm moles}{1 \;\rm mole}\\\\&= 0.530 \;\rm J \end{aligned}[/tex]
Convert joules to kilo joules as:
1 kJ = 1000 J
? = 0.530 J
Solving the conversion:
[tex]\begin{aligned} & =\dfrac{0.530\;\rm J}{100 \;\rm J} \times 1 \;\rm kJ\\\\&= 5.30 \times 10^{-4} \;\rm kJ\end{aligned}[/tex]
Therefore, [tex]5.30\times 10^{-4} \;\rm kJ[/tex] is the enthalpy of the reaction.
Learn more about enthalpy here:
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