Sodium hydroxide (NaOH) has a lattice energy of -887 kJ>mol and a heat of hydration of -932 kJ>mol. How much solution could be heated to boiling by the heat evolved by the dissolution of 25.0 g of NaOH? (For the solution, assume a heat capacity of 4.0 J>g # °C, an initial temperature of 25.0 °C, a boiling point of 100.0 °C, and a density of 1.05 g>mL.)

Video transcript

hey everyone. So here it says the lattice energy and heat of hydration for lithium hydroxide are negative 10 21 kg per mole and negative 10 44. kg per mole respectively, Calculate the volume of the solution that can be heated to boiling by the heat evolved by the dissolution of 42.5 g of lithium hydroxide. Here we're assuming the heat capacity of the solution is 4.20 jewels over Graham's time degrees Celsius that its initial temperature is 27 degrees Celsius. Its boiling point is 100 degrees Celsius and its density is 1.5 g per milliliter. Alright, so first we're going to say here that are entropy of dissolution is equal to negative entropy of lattice energy plus entropy of hydration. Now, from the information given to us within the question, this will come out to negative negative 10 21 kg joules per mole plus a negative 44.5 kg joules per mole. Which comes out to negative 23.5 kg per mole. Now, next we're going to say that are moles and times are entropy of dissolution equals m cat Now. And as our moles were given 42.5 g of lithium hydroxide, We're gonna first change those grams into moles. So one mole of lithium hydroxide weighs approximately 23.948g. So here grams of lithium hydroxide cancel out this will be our end, We're going to multiply by our entropy of dissolution, which is 23,500 jewels per mole equals mass, which is what we need to find times the entropy the heat capacity given to us which is 4.20 g over jewels. Over grams times degrees Celsius. Our final temperature is 100°C, which is our boiling - Our initial temperature of 27°C. Alright, so we're gonna have our moles multiply with our entropy of dissolution. We're gonna have our specific heat capacity multiplied bar change in temperature. This is gonna help us to basically reduce this down in simpler terms. So on this side it's 41,704.944 jewels equals m Times six g jewels over g. Alright, so now we need to isolate our mass when we isolate our mass by dividing both sides by 306.6 we get mass equals 1 36.02 g. Remember here that density equals mass over volume. Thanks. And if we rearrange it we can isolate volume. So volume here equals mass over density. So that's 1 36.02 g Divided by 1.05 g over ml. Here. My grams will cancel out And we'll have our middle leaders at the end which come out to 129.5 ml. So this will be our final answer