Under special conditions, sulfur reacts with anhydrous liquid ammonia to form a binary compound of sulfur and nitrogen. The compound is found to consist of 69.6% S and 30.4% N. Measurements of its molecular mass yield a value of 184.3 g/mol. The compound occasionally detonates on being struck or when heated rapidly. The sulfur and nitrogen atoms of the molecule are joined in a ring. All the bonds in the ring are of the same length. (a) Calculate the empirical and molecular formulas for the substance.

Video transcript

Hey everyone, we're told a substance is composed of 43.64% of phosphorus and 56.36% of oxygen. It has a molar mass of 283.88 g per mole and were asked to provide the empirical and molecular formula. First, we can go ahead and assume that we have 100 g since our percentages right here Total up to 100%. And this will make it easier for us to convert from percentages into g. Starting off with our phosphorus, we're going to take that 43.64% and convert it into grams of phosphorus. Using the molar mass of phosphorus, we can go ahead and use our dimensional analysis and convert from grams into moles. So looking at our periodic table, we know that we have 30.97 g of phosphorus per one mole of phosphorus. Now, when we calculate this out and cancel out our units, we end up with a total of 1. mole of phosphorus. Moving on to our oxygen, We're going to take 56.36% and convert it into grams of oxygen. And again, looking at our periodic table, we know that we have 16 g of oxygen Per one mole of oxygen. When we cancel out our units and calculate this out, we end up with a total of 3.52- mole of oxygen. Now in order to figure out our empirical formula, we need to divide each of these values by the least amount of mold that we have here in this case it's going to be 1.4091 from our phosphorus. So when we calculate this out, we end up with a total of one of phosphorus And 2.5 of our oxygen. Now, since we need whole numbers, we can go ahead and multiply each of these values by two and this will get us to two of phosphorus and five of our oxygen. Now, our empirical formula is going to come up two p 205. Now let's go ahead and calculate our molecular formula first, we need to calculate the molar mass of our empirical formula. So we have two of phosphorus and we're going to multiply it by its molar mass of 30.97 g per mole. This will get us to 61.94 g per mole. Now looking at our oxygen, we have five of oxygen and we're going to multiply it by its smaller mass of 16.0 g per mole. This will get us to a total of 80 g Permal. Now, when we add these two values up, we end up with a total of 141.94 g per mole of our empirical formula, which is P 205. To calculate our molecular formula, We can go ahead and take that molar mass of 283.88 g per mole. That was provided to us from our question stem, And we can divide it by that 141.94 g per mole, which is the molar mass of our empirical formula. And when we calculate this out, we end up with a value of two. So this means that we're going to go ahead and take our empirical formula of P 205 and multiply it by two, Which will get us to P 4010. And this is going to be our molecular formula. Now, I hope that made sense and let us know if you have any questions.