The solid oxide of generic metal M is added to 75 mL of water and reacts to produce a basic solution that is 0.20 M in the resulting compound. Neutralization of the solution required titration with 27 mL of 0.56 M HCl. How many valence electrons must M have?
To determine the number of valence electrons that the metal M must have, we need to analyze the reaction and the stoichiometry of the compounds involved.
First, let's write the balanced chemical equation for the reaction:
MxOy + H2O -> M(OH)z
Based on the information given, we know that the resulting solution is basic, which indicates that the product (M(OH)z) is a base. Therefore, M(OH)z can be considered a metal hydroxide.
From the concentration given (0.20 M) and the volume of the resulting solution (75 mL), we can calculate the number of moles of M(OH)z produced:
Moles of M(OH)z = Concentration * Volume
= 0.20 M * 75 mL
= 0.015 moles
Since the balanced equation tells us that 1 mole of M(OH)z is formed from 1 mole of MxOy, we can conclude that 0.015 moles of MxOy reacted.
Now let's calculate the number of moles of HCl required for neutralization:
Moles of HCl = Concentration * Volume
= 0.56 M * 27 mL
= 0.015 moles
From the balanced equation, we can see that 1 mole of HCl reacts with 1 mole of M(OH)z. Therefore, the number of moles of HCl used is equal to the number of moles of M(OH)z formed.
Now, we need to determine the chemical formula of MxOy to find the valence of M. To do this, we need to calculate the molar mass of MxOy using the moles and mass of MxOy.
Molar mass of MxOy = Mass / Moles
Since the molar mass of oxygen is 16 g/mol, and the mass of the oxygen in the reaction is (y * 16 g/mol), we can write:
Mass of MxOy = Molar mass of MxOy * Moles + (y * 16 g/mol)
To get the mass, we can subtract the mass of oxygen from the total mass:
Mass of M = Mass of MxOy - (y * 16 g/mol)
Finally, we can use the periodic table to determine the number of valence electrons associated with the atomic number of M.
In summary, to find the number of valence electrons, we need to calculate the molar mass of MxOy, determine the mass of M, and use the periodic table to find the number of valence electrons based on the atomic number of M.