**Solution:**

To determine the value of x in the metal chloride MClx, we need to use the concept of stoichiometry and the reaction between MClx and AgNO3.

**Stoichiometry:**

Stoichiometry is the calculation of the quantities of reactants and products involved in a chemical reaction. It involves determining the molar ratios between the reactants and products based on the balanced chemical equation.

**Balanced Chemical Equation:**

The balanced chemical equation for the reaction between MClx and AgNO3 can be represented as follows:

MClx + AgNO3 → AgCl + M(NO3)x

**Given Information:**

- Concentration of MClx solution = 0.1 M
- Volume of MClx solution used = 500 ml (or 0.5 L)
- Concentration of AgNO3 solution = 0.6 M
- Volume of AgNO3 solution used = unknown

**Using Stoichiometry:**

In the given reaction, the stoichiometric ratio between MClx and AgNO3 is 1:1. This means that for every 1 mole of MClx, 1 mole of AgNO3 is required for complete precipitation.

Using the concentration-volume relationship, we can determine the number of moles of MClx present in the solution used:

Moles of MClx = concentration of MClx × volume of MClx solution
= 0.1 M × 0.5 L
= 0.05 moles

Since the stoichiometric ratio is 1:1, the number of moles of AgNO3 required for complete precipitation is also 0.05 moles.

Using the concentration-volume relationship for AgNO3, we can determine the volume of AgNO3 solution required:

Volume of AgNO3 solution = moles of AgNO3 / concentration of AgNO3
= 0.05 moles / 0.6 M
= 0.0833 L (or 83.3 ml)

Therefore, the volume of 0.6 M AgNO3 solution required for complete precipitation is 83.3 ml.

**Conclusion:**

Since the given information states that 500 ml of 0.6 M AgNO3 solution is required for complete precipitation, but the calculated volume is 83.3 ml, it suggests that there is an excess of AgNO3 in the reaction. This excess AgNO3 is required to ensure the complete precipitation of MClx.

As a result, the value of x in the metal chloride MClx is not determined by this experiment. Additional information or experiments would be necessary to determine the value of x.

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