2.34g of magnesium nitrate is dissolved in water and the total volume of the solution is made up to 250cm^3.How many nitrate ions does 100cm^3 of the solution contain?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The molecular formula of magnesium nitrate is `Mg(NO_3)_2` . Each molecule of magnesium nitrate gives two nitrate ions. The molar mass of magnesium nitrate is 148.32 g.

2.34 g of magnesium nitrate is dissolved in water and the total volume of the solution is made up to 250 cm^3. 100 cubic cm of the solution has `2.34/2.5 = 0.939` g of magnesium nitrate. 0.939 g of magnesium nitrate is equivalent to `0.939/148.32 = 13/2060` moles. Each mole of a substance has approximately 6.022*10^23 elementary entities. `13/2060` moles of magnesium nitrate dissociates to gives `26/2060*6.022*10^23 ~~ 0.076*10^23` nitrate ions.

There are 0.076*10^23 nitrate ions in 100 cubic centimeter of the solution.

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science2014 | (Level 1) Valedictorian

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Molecular weight (MW) of magnesium nitrate = 148.3 g/mol

So 2.34 g magnesium nitrate corresponds to (2.34 / 148.3) moles = 0.016 moles

This much moles are present in a solution of 250 cm^3 or 250 c.c

= 250 / 1000 L (as 1000 c.c. = 1 L)

= 0.25 L

So the concentration of the solution = 0.016 moles / 0.25 L

= 0.016 / 0.25 moles / L  (i.e. M)

= 0.064 M

Thus, 100 cm^3 = 100 / 1000 L = 0.1 L of the solution will contain

0.064 * 0.1 moles = 0.0064 moles of magnesium nitrate

As one mole of magnesium nitrate dissociates into 2 moles of nitrate ion,

the 100 cm^3 solution will contain 0.0064 * 2 moles of nitrate

We know that one mole of a substance contains Avogadro number (6.023 * 10^23) of particles in it.

This means one mole of nitrate contains 6.023 * 10^23 nitrate ions

Thus, 0.0064 * 2 moles of nitrate contains 0.0064 * 2 * 6.023 * 10^23 moles of nitrate ions

= 0.077 * 10^23 moles of nitrate ions

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