Question

The solid oxide of generic metal M is added to 75 mL of water and reacts to produce a metal hydroxide solution that is 0.40 M in the resulting compound. The metal hydroxide solution then reacts with all of the 27 mL of 1.1 M HCl to form water and the metal salt. How many valence electrons must M have?

Answer 1

Answer: The number of valence electrons that M must have is 1.

Step-by-step explanation:

The chemical equation for the reaction of metal oxide with water follows:

`\text{Metal oxide}+H_2O\rightarrow M(OH)_x`

The reaction of metal hydroxide with hydrochloric acid follows:

`M(OH)_x+xHCl\rightarrow MCl_x+xH_2O`

To calculate the number of moles for given molarity, we use the equation:

`\text{Molarity of the solution}=\frac{\text{Moles of solute}* 1000}{\text{Volume of solution (in mL)}}` .....(1)

• For metal hydroxide:

Molarity of metal hydroxide solution = 0.40 M

Volume of solution = 75 mL

Putting values in equation 1, we get:

`0.40=\frac{\text{Moles of }M(OH)_x* 1000}{75}\\\\\text{Moles of }M(OH)_x=(0.40* 75)/(1000)=0.03mol`

• For HCl:

Molarity of HCl = 1.1 M

Volume of solution = 27 mL

Putting values in equation 1, we get:

`1.1=\frac{\text{Moles of HCl}* 1000}{27}\\\\\text{Moles of HCl}=(1.1* 27)/(1000)=0.0297mol`

To calculate the value of 'x', we divide the number of moles of HCl by number of moles of metal hydroxide, we get:

`x=\frac{\text{Moles of HCl}}{\text{Moles of }M(OH)_x}\\\\x=(0.0297)/(0.03)=0.99\approx 1`

Hence, the number of valence electrons that M must have is 1.