Calculate Molar Enthalpy Change for Magnesium & Copper Sulphate Reaction

[mouk92]

Homework Statement

Magnesium will also displace copper from copper (II) sulphate solution. If an excess of magnesium is added to 100 cm3 of 1.0 moldm-3 copper(II) sulphate, the temperature increases by 46.3 oC.

a) Calculate the molar enthalpy change for the reaction

b) Calculate the minimum quantity of magnesium required to ensure it is in excess.

c) Calculate the temperature change if only 0.8 g of magnesium is added.

Homework Equations

Q=m*c *DT
Moles=concentration*volume
DH=q in KJ/moles

The Attempt at a Solution

a) Calculate the molar enthalpy change for the reaction. ( i got the answer to be -193.534 KJmol -1 )

However I am stuck on the rest of this question...

b) Calculate the minimum quantity of magnesium required to ensure it is in excess.
c) Calculate the temperature change if only 0.8 g of magnesium is added.thanks.

 

[vertciel]

Hello there,

I will start by writing the chemical equation:

Mg + Cu(SO₄)₂ -> Cu + Mg(SO₄)₂

b) For this part, you know that Mg is in excess. Therefore, you simply need to find the amount of Cu(SO₄)₂ in mols. When you have this, then you know that the excess amount of Mg will be anything > the amount of Cu(SO₄)₂ because Cu(SO₄)₂ is the limiting reagent.

c) You know that Q = mc∆T.

You know the specific heat capacity, mass of magnesium, and you can calculate Q. Since you know the heat enthalpy, you can multiply this value by the mols of magnesium used to find the heat energy evolved from adding this magnesium.

Now, you just need to rearrange the above equation for ∆T and solve.

I hope that this helps!

 

[Blueshift5]

a) To calculate the molar enthalpy change, we can use the formula DH=q/moles. We already have the value for DH (46.3 oC), so we just need to calculate the moles of copper(II) sulphate used in the reaction. We can use the equation moles=concentration*volume to find the moles of copper(II) sulphate. 1.0 moldm-3 is the same as 1 mol/L, so we can multiply the concentration by the volume in liters to get the moles. 1.0 mol/L * 0.1 L = 0.1 moles. Now we can plug this value into the formula DH=q/moles: DH=46.3 oC/0.1 moles=463 KJ/mol. However, we need to convert the temperature from oC to Kelvin, so we add 273 to get 736 KJ/mol. Therefore, the molar enthalpy change for the reaction is 736 KJ/mol.

b) To calculate the minimum quantity of magnesium required, we need to use the balanced chemical equation for the reaction:

Mg + CuSO4 → MgSO4 + Cu

From the equation, we can see that for every 1 mole of magnesium, 1 mole of copper(II) sulphate is required. We already calculated the moles of copper(II) sulphate in part a) to be 0.1 moles. So, we need at least 0.1 moles of magnesium to ensure it is in excess. To convert this to grams, we use the molar mass of magnesium (24.31 g/mol). 0.1 moles * 24.31 g/mol = 2.43 g of magnesium is the minimum quantity needed to ensure it is in excess.

c) To calculate the temperature change if only 0.8 g of magnesium is added, we first need to calculate the moles of magnesium using its molar mass (24.31 g/mol). 0.8 g / 24.31 g/mol = 0.033 moles of magnesium. Now we can use the formula DH=q/moles to find the temperature change: DH=46.3 oC/0.033 moles = 1403 KJ/mol. Again, we need to convert the temperature to Kelvin by adding 273, so the temperature