A 600-milliliter solution contains 10.1 grams of magnesium chloride. What is the molar concentration of magnesium chloride in this solution?
What we have here is 600 milliliters or 0.6 liters of a solution of magnesium
chloride. Magnesium chloride has the formula MgCl₂. That’s one magnesium ion and two chloride ions. Magnesium is in group two and therefore loses two electrons to form Mg²⁺. Chlorine is in group 17 and gains one electron to form Cl⁻. We need two chloride ions to make an overall neutral magnesium chloride ionic
What this question is asking for is the concentration of magnesium chloride in the
solution. A molar concentration has units of moles per liter, otherwise given the letter
𝑀. However, we’ve been given the mass of magnesium chloride, not the number of
moles. So one thing you should definitely not do is work out the mass concentration in grams
So the first thing we need to do to answer this question is to calculate the number
of moles of magnesium chloride in 10.1 grams. Then we can calculate the concentration of magnesium chloride. To work out the number of moles, we can use the formula 𝑛 equals little 𝑚 over big
𝑀, where 𝑛 is equal to the number of moles. Little 𝑚 is equal to the mass of the substance in grams. And big 𝑀 is equal to the molar mass in grams per mole.
To do the first step, we need to know the molar mass of magnesium chloride. This is equal to the atomic mass of magnesium plus two equivalents of the atomic mass
of chlorine. We need two equivalents of the atomic mass of chlorine, because we have two
equivalents of chloride ions per magnesium chloride unit. We can look up the values of these in our periodic table.
The relative atomic mass of magnesium is 24.305. So the molar atomic mass of magnesium is 24.305 grams per mole. The molar mass of chlorine is 35.45 grams per mole. Completing this calculation gives us a molar mass of magnesium chloride of 95.205
grams per mole.
Now we need to do is substitute values into our equation 𝑛 equals 𝑚 over 𝑀. We divide 10.1 grams of magnesium chloride by 95.205 grams per mole, which is equal
to about 0.1 moles of magnesium chloride. Now we need to calculate the concentration of magnesium chloride using the formula 𝐶
equals 𝑛 divided by 𝑉, where 𝐶 is the concentration in molar. 𝑛 is the number of moles. And 𝑉 is the volume in liters.
However, we’ve been given the volume of solution in milliliters. The prefix “m” means 10 to the minus three of something. So 600 milliliters equals 600 times 10 to the minus three liters or 0.6 liters. Another way of looking at this is that 1000 milliliters is equivalent to one
Now we can substitute our values into the formula 𝐶 equals 𝑛 divided by 𝑉. So we divide 0.106087 by 0.6, which is equal to 0.176811 molar. The values in the question are all to three significant figures. So we should round our answer to the same degree of precision. Therefore, the molar concentration of magnesium chloride when 10.1 grams of magnesium
chloride is in 600 milliliters of solution is 0.177 molar.