Video Transcript
Titanium metal can be produced by reacting titanium chloride with magnesium metal. The reaction also produces magnesium chloride, MgCl2. The formula for titanium chloride could be TiCl, TiCl2, TiCl3, or TiCl4. If 6.1 kilograms of magnesium produces 6.0 kilograms of titanium, what is the correct formula for titanium chloride in this reaction? The molar mass of titanium is 48 grams per mole, magnesium is 24 grams per mole, and chlorine is 35.5 grams per mole.
In order for us to solve this problem, let’s first begin by writing a chemical equation for the reaction. In the first sentence of the question, we can see that the reactants are titanium chloride and magnesium metal. Because in this question we do not know the exact chemical formula for titanium chloride, let’s write an 𝑥 after Cl in the formula. The chemical symbol for magnesium metal is Mg. According to the question, the products of the reaction are titanium metal and magnesium chloride.
The chemical symbol of titanium is Ti. And we are given the chemical formula of magnesium chloride, which is MgCl2. Because we don’t know the chemical formula of the first reactant, titanium chloride, we can’t balance our equation yet. However, we do know that when 6.1 kilograms of magnesium reacts, 6.0 kilograms of titanium are produced. We typically work with the mass unit grams in stoichiometry problems. So, let’s go ahead and convert each mass into grams. We can do this by taking the mass in kilograms and multiplying by 1000 grams per kilogram. This gives us 6100 grams of magnesium and 6000 grams of titanium.
Now, if we were to convert the mass of magnesium and titanium to moles, then we could determine the molar ratio of magnesium to titanium and begin to balance the chemical equation. The molar ratio is the ratio of the amount in moles of two substances involved in a chemical reaction. The amount of moles of each substance is represented by the stoichiometric coefficients used to balance the equation.
To convert from grams of magnesium to moles of magnesium, we need to divide by the average molar mass of magnesium provided in the problem, which is 24 grams per mole. After dividing and rounding to the nearest whole number, the result is 254 moles of magnesium. To convert grams of titanium to moles of titanium, we’ll divide by the average molar mass of titanium provided in the problem, which is 48 grams per mole. After dividing and rounding to the nearest whole number, the result is 125 moles of titanium.
Now, let’s write the molar ratio of magnesium to titanium. We can start by writing the ratio 254 to 125. Next, let’s divide both sides of our ratio by the smaller amount of moles, which is 125. After dividing and rounding to the nearest whole number, the reduced ratio is two to one. Now we can write a coefficient of two in front of magnesium and a coefficient of one in front of titanium in our equation. However, a coefficient of one in chemistry is assumed, and therefore we don’t need to write it. Now, let’s balance the rest of the chemical equation.
Let’s take a look at the number of magnesium atoms first. On the reactant side of the equation, there are two magnesium atoms. And on the product side, there is only one magnesium atom. Therefore, we’ll need to write a coefficient of two in front of magnesium chloride. Now, let’s balance the titanium atoms. On the product side of the equation, we know there is only one atom of titanium. Therefore, the coefficient in front of titanium chloride on the reactant side should also be one.
Finally, let’s balance the chlorine atoms. On the product side, there are a total of two times two, or four, chlorine atoms. On the reactant side, since we know that there is a coefficient of one in front of titanium chloride, this means that the 𝑥 in the titanium chloride formula must be four.
Therefore, the correct chemical formula of titanium chloride in the reaction described in this question is TiCl4.
