Question

A 1.00-g sample of an alkaline earth metal chloride is treated with excess silver nitrate. All of the chloride is recovered as 1.38 g of silver chloride. Identify the metal.

Short answer

The alkaline earth metal in the chloride sample is Calcium (Ca).

Step-by-step solution

Find the moles of silver chloride and chloride ions

First, we need to determine the moles of silver chloride (AgCl) formed in the reaction. We are given the mass of silver chloride as 1.38 g, and we can find the molar mass of AgCl to be 107.87 g/mol (Ag) + 35.45 g/mol (Cl) = 143.32 g/mol (AgCl). Now, we can calculate the moles of AgCl formed: moles of AgCl = \( \frac{mass}{molar \:mass} \) moles of AgCl = \( \frac{1.38\: g}{143.32\: g/mol} \) = 0.00962 mol of AgCl Since AgCl dissociates into Ag and Cl ions in a 1:1 ratio, we therefore have exactly the same amount of chloride ions formed, that is 0.00962 mol of chloride ions.

Calculate the moles of alkaline earth metal chloride

We are given that the mass of the alkaline earth metal chloride is 1.00 g. Let MCl2 represent the metal chloride, where M is the alkaline earth metal and Cl2 is the chloride. The chloride content in MCl2 is the same as in the 1.38 g of AgCl, which means we have 0.00962 mol of chloride ions in the metal chloride sample. Since the ratio of M to Cl2 in MCl2 is 1:1, we therefore have 0.00962/2 = 0.00481 mol of the metal in MCl2.

Calculate the molar mass of the alkaline earth metal

Now we have the moles of the alkaline earth metal in MCl2, and we are given the mass of MCl2, 1.00 g. From this information, we can determine the molar mass of the alkaline earth metal: molar mass of M = \( \frac{mass \:of \:MCl2 - mass \:of \:Cl2}{moles \:of \:M} \) molar mass of M = \( \frac{1.00\: g - (0.00962 \:mol \times 35.45\: g/mol)}{0.00481\: mol} \) = 40.34 g/mol

Identify the alkaline earth metal

With the calculated molar mass of 40.34 g/mol, we can identify the alkaline earth metal by comparing it to the molar mass of known alkaline earth metals: 1. Be (Beryllium): 9.01 g/mol 2. Mg (Magnesium): 24.31 g/mol 3. Ca (Calcium): 40.08 g/mol 4. Sr (Strontium): 87.62 g/mol 5. Ba (Barium): 137.33 g/mol 6. Ra (Radium): 226.03 g/mol Comparing the obtained molar mass of the alkaline earth metal (40.34 g/mol) with the molar masses above, we can deduce that the metal is Calcium (Ca) as its molar mass is closest to our calculated value. Therefore, the alkaline earth metal in the chloride sample is Calcium.

Key concepts

Molar Mass Calculation

Molar mass calculation is an essential skill for understanding chemistry, especially when it comes to analyzing chemical compounds.
It allows us to determine how much of a substance is present in a given amount of another substance. By knowing the composition of a compound and the atomic masses of its constituent elements, we can find the molar mass.
For instance, calculating the molar mass of silver chloride (AgCl) was the critical first step in the problem exercise. Silver (Ag) has a molar mass of 107.87 g/mol, while chlorine (Cl) is 35.45 g/mol.

• To find the molar mass of AgCl, we simply add these two values together, resulting in 143.32 g/mol.


• This allowed us to determine the moles of silver chloride, given its mass in the original exercise.

This type of calculation is a gateway to understanding more complex chemical behavior and reactions.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry involves using the relationships between reactants and products in a chemical reaction.
It helps us understand how much of each substance is needed or produced. In our exercise, stoichiometry was used to bridge information between silver chloride and the chloride ions derived from the alkaline earth metal chloride.
The given mass of silver chloride was 1.38 g, and knowing its molar mass, we were able to compute the moles of AgCl.

• Since silver chloride dissociates into silver (Ag) and chloride ions (Cl), the reaction was considered 1:1 for each ion.


• Through this stoichiometry, we deduced that the moles of chloride ions were equal to those of AgCl, 0.00962 moles.

Understanding stoichiometry allows you to see how different parts of a reaction are interconnected and how a change in one aspect can affect others.

Chemical Identification

Chemical identification is used to determine what elements or compounds are present in a sample.
In the exercise, we used the calculated molar mass of the mystery metal to identify it. After determining the moles of the alkaline earth metal chloride (MCl2) and its total mass, we could compute the molar mass of the alkaline earth metal involved.
Knowing that the molar mass was approximately 40.34 g/mol, we compared this with known alkaline earth metals:

• Beryllium (Be) has a molar mass of 9.01 g/mol.


• Magnesium (Mg) has a molar mass of 24.31 g/mol.


• Calcium (Ca) has a molar mass of 40.08 g/mol, which closely matched our calculated value.


• Strontium (Sr) and Barium (Ba) have much higher molar masses.

By this process of elimination, we concluded that the metal involved was calcium.