For two questions below, first write and balance the equation for the chemical reaction.  Please, also review the material in Chapter 8, if you will feel you might need it in order to answer the questions. 

Next, please answer the following questions:
(a) What substance is reduced?
(b) What is the reducing agent?
(c) What substance is oxidized?
(d) What is the oxidizing agent?

Question 1:   Erbium metal (Er) can be prepared by reacting erbium(III) fluoride with magnesium; the other product is magnesium fluoride.
2 ErF3 + 3 Mg → 3 MgF2 + 2 Er
a) 2ErF3
b) 3Mg is oxidized to 3MgF2
c) 3Mg
d) 2ErF3 is reduced to 2Er

Question 2:  Europium (Eu) is used in older television screens to give a red color. The metal can be prepared by electrolysis of molten europium(III) chloride; chlorine gas is a by-product.
2EuCl3 --> 2Eu + 3Cl2
a)
b)
c)
d)

Not sure what I have right or wrong. need help please.

First, I have no idea what Chapter 8 says.

For question 1, your answers look ok although I wouldn't have answered them exactly as you did. For example, I think ErF3 is reduced. Although 2ErF3 isn't wrong, at least I wouldn't count that wrong on an exam, I would omit the 2. Same for the other answers.

For 2.
Since I've told you that your answers are ok for 1, 2 is done the same way.

Let's analyze the given chemical reaction equations to find the answers to the questions:

Question 1: Erbium metal (Er) can be prepared by reacting erbium(III) fluoride with magnesium; the other product is magnesium fluoride.

2 ErF3 + 3 Mg → 3 MgF2 + 2 Er

(a) What substance is reduced?
In this reaction, erbium(III) fluoride (ErF3) is reduced.

(b) What is the reducing agent?
The reducing agent is the substance that causes the reduction. In this case, magnesium (Mg) is the reducing agent, as it gives electrons to ErF3, causing its reduction.

(c) What substance is oxidized?
In this reaction, magnesium (Mg) is oxidized.

(d) What is the oxidizing agent?
The oxidizing agent is the substance that causes the oxidation. In this case, erbium(III) fluoride (ErF3) is the oxidizing agent, as it accepts the electrons from Mg during the oxidation process.

Question 2: Europium (Eu) is used in older television screens to give a red color. The metal can be prepared by electrolysis of molten europium(III) chloride; chlorine gas is a by-product.

2 EuCl3 → 2 Eu + 3 Cl2

(a) What substance is reduced?
In this reaction, europium(III) chloride (EuCl3) is reduced.

(b) What is the reducing agent?
The reducing agent is the substance that causes the reduction. In this case, there is no explicit reducing agent mentioned in the equation. However, the source of electrons for reduction in electrolysis is usually the cathode (negative electrode). So, we can assume that the cathode is the reducing agent.

(c) What substance is oxidized?
In this reaction, chlorine gas (Cl2) is oxidized.

(d) What is the oxidizing agent?
The oxidizing agent is the substance that causes the oxidation. In this case, there is no explicit oxidizing agent mentioned in the equation.

Please note that the information provided in this explanation is based solely on the given chemical reactions equations and might require additional information from Chapter 8 to provide a comprehensive answer.

Question 1:

The balanced equation for the reaction is:
2 ErF3 + 3 Mg → 3 MgF2 + 2 Er

(a) The substance that is reduced is 2 ErF3.
(b) The reducing agent is 3 Mg.
(c) The substance that is oxidized is 3 Mg.
(d) The oxidizing agent is 2 ErF3.

Question 2:
The balanced equation for the reaction is:
2 EuCl3 → 2 Eu + 3 Cl2

(a) The substance that is reduced is 2 EuCl3.
(b) The reducing agent is not specified in this case.
(c) The substance that is oxidized is not specified in this case.
(d) The oxidizing agent is not specified in this case.

Hope this helps! Let me know if you have any further questions.