A 10.0 M aqueous solution of NaOH has a density of 1.33 g/cm3 at 25 C. Calculate the mass percent of the NaOH in the solution (a) 53.2% (b) 30.1% (c) 40.0% (d) 13.3%

Video transcript

Hello everyone today. We have the following problem at 20°C. The density of a six smaller solution of hydrochloric acid in water is 1.098g per middle leader determine the mass percent of hydrochloric acid in the quickest solution. So First we want to jot down the molar mass of hydrochloric acid, which according to the periodic table, will result in a molar mass of 36. g per mole. We're gonna hang onto this number for later. Next we're going to find how many moles of hydrochloric acid we have and so we can do that by taking our six molar solution which will be in units of moles per liter. So we have six moles of hydrochloric acid over one leader of hydrochloric acid, Multiplied by one leaders of solution. And so it's important that we assume that we have one leader as a solution to simplify for answers and so we cancel this out. We note that we have just six moles of hydrochloric acid. So we'll keep that number for later from those moles. We're gonna go ahead and find our mass of hydrochloric acid that we have present. So we're gonna take our six moles Of hydrochloric acid. And we're going to multiply by the molar mass that we found earlier, which was 36.458g of hydrochloric acid in one mole of hydrochloric acid. And when our units of moles per hydrochloric acid cancel out, we will get 218.748g of hydrochloric acid. We can save that number there. Our second to last step is going to be to find the mass of our solution. So we found the mass over H C. O. Now we need to find the mass of our solution And so we can do that because we said that we're going to assume that we have one leader solution. So it's going to be 1000 ml. And we're gonna multiply that 1000 ml by the density. And the density was said to be 1. grams per one middle liter. When our unions of milliliters canceled out. We're left with 1098 g of our solution. And so we're gonna hang on to that number for later. And our last step we can now determine the mass percent of a hydrochloric acid in the solution. And we can do that by taking The mass of hcl that we found which is 218. grams of hydrochloric acid. And we can divide that by our mass of our solution which was 1,098 g of our solution. And we're also gonna multiply that by 100 because it is percentages And that's going to lead us with an answer of 19 0. percent. And if we notice in our answer choices that is going to lead us with. Andrew choice a overall I hope this helped. And until next time