Video Transcript
Consider the equation two NaOH aqueous plus MgCl2 aqueous makes two NaCl aqueous plus Mg(OH)2 solid. From the equation, what is the mass of NaOH when five grams of Mg(OH)2 precipitates? Give you answer to one decimal place. The molar mass of sodium is 23 grams per mole, oxygen is 16 grams per mole, hydrogen is one gram per mole, and magnesium is 24 grams per mole.
In this question, we can see that a solution of sodium hydroxide is being reacted with a solution of magnesium chloride. Both of these compounds are very soluble in water. This reaction produces a sodium chloride solution and a white precipitate of magnesium hydroxide. We can tell magnesium hydroxide is a precipitate in this reaction by looking carefully at the state symbols in the balanced equation. Magnesium hydroxide is represented with an s for solid.
We’re told that five grams of magnesium hydroxide precipitate is being collected. The five grams has been measured after the precipitate has been washed with distilled water and dried to constant mass. We need to find the mass of sodium hydroxide in one of the original solutions that caused this mass of precipitate to be formed. We can relate the mass of magnesium hydroxide formed to the mass of sodium hydroxide reacting in this equation using the molar ratio or stoichiometry.
From the balanced equation, we can see that two moles of sodium hydroxide always forms one mole of magnesium hydroxide in this reaction. This will always happen when the sodium hydroxide reacts with excess magnesium chloride. This is the assumption we’re going to make here. Since we have the mass of magnesium hydroxide in grams, we can calculate how many moles this equates to. To find the moles of magnesium hydroxide, we’ll use the equation moles equals mass of substance in grams divided by the molar mass in grams per mole. To find the molar mass of magnesium hydroxide, we sum together the average molar masses of the constituent atoms in this substance.
According to the formula of magnesium hydroxide, it contains one magnesium atom, two oxygen atoms, and two hydrogen atoms per formula unit. By summing together the average molar masses for the atoms concerned in magnesium hydroxide, we find its molar mass is 58 grams per mole. The moles of magnesium hydroxide formed becomes five grams divided by 58 grams per mole. Using a calculator, the moles of magnesium hydroxide is therefore approximately 0.0862.
Now, we’re in a position to use the molar ratio to find the moles of sodium hydroxide that was involved in this reaction. The molar ratio for sodium hydroxide to magnesium hydroxide is two to one. For every one mole of magnesium hydroxide formed, there would’ve been two moles of sodium hydroxide reacting. We therefore need to double the moles of magnesium hydroxide to find the moles of sodium hydroxide to answer the question. The moles of sodium hydroxide reacting is therefore approximately 0.1724 moles.
We now need to convert the moles of sodium hydroxide into a mass of sodium hydroxide to answer this question. To do this, we’ll use the equation mass equals moles times molar mass. It’s the molar mass of sodium hydroxide that we need to find next. To find the molar mass of sodium hydroxide, we’ll sum together the average molar masses of its constituent atoms just as we did for magnesium hydroxide before. Per formula unit, sodium hydroxide contains one sodium atom, one oxygen atom, and one hydrogen atom. By summing together the average molar masses of the atoms concerned, we find that the molar mass of sodium hydroxide is 40 grams per mole. In the calculation, the mass of sodium hydroxide is approximately 0.1724 moles multiplied by 40 grams per mole. So the mass of sodium hydroxide is found to be approximately 6.8965 grams.
It’s very important that we comply with the question and give our answer to one decimal place. Presenting our answer to one decimal place, we get 6.9 grams as the mass of sodium hydroxide. 6.9 grams is the correct answer.
