Imagine that you dissolve 10.0 g of a mixture of NaNO3 and KF in 100.0 g of water and find that the temperature rises by 2.22 °C. Using the following data, calculate the mass of each compound in the original mixture. Assume that the specific heat of the solution is 4.18 J1 g °C2
NaNO31s2 S NaNO31aq2 ΔH = + 20.4 kJmol
KF1s2 S KF1aq2 ΔH = - 17.7 kJmol

Question

Imagine that you dissolve 10.0 g of a mixture of NaNO3 and KF in 100.0 g of water and find that the temperature rises by 2.22 °C. Using the following data, calculate the mass of each compound in the original mixture. Assume that the specific heat of the solution is 4.18 J>1 g °C2 
NaNO31s2 S NaNO31aq2 ΔH = + 20.4 kJ>mol 
KF1s2 S KF1aq2 ΔH = - 17.7 kJ>mol

Accepted Answer

Hello everyone today. We are being asked the following question, a 15 g mixture of lithium chloride and potassium nitrate are dissolved in 150 g of water causing the temperature to increase by 1.68°C. Using the heats of dissolution of each component, calculate the mass of each component of the mixture. Use the specific heat of water for the solution. So the first thing that we want to do is you want to calculate the energy of our two components lithium chloride, in our potassium nitrate. Starting with our lithium chloride, we have our heat of dissolution here, we have -37.03 kg per mole. And this can be found in a reference text. We're going to convert our units of we're gonna try and get rid of our units of moles so I think we can get kilo jewels programs. And so this is gonna be one mole is equal to 42.39 4 g. And this is the molar mass for lichen chloride For the periodic table. And when our units cancel out and we calculate this, we get .8735 kg jewels program. Next, we need to calculate the energy for potassium nitrate. So we're gonna go through the same procedure here, But instead we're going to use 34.89 kilograms per mole And then use the same conversion of one mole is equal to 101.103g. And through calculation and unit cancelation running at .3451 kg joules per gram. We're gonna use these numbers for later. Next we're going to calculate the overall heat of our solution. And so that's gonna be represented by Q. Of the solution. That is equal to our mass. Times specific heat capacity times the change in our temperature. So our mass is going to be that 15 g of that mixture plus the 150 g of water that we have times the specific heat of water which is in the reference texas 4. joules per grams Celsius Multiplied by the change in temperature. And it was noted that this temperature increased by 1.68°C. When we do that We get 1,158.7 jewels. Which you must then convert to kill a jewels by using the conversion factor That one killer jewel is equal to 1000 jewels. We then get 1.1587 kg jewels. We're gonna hang on to that number there. And so now we have our heat of our reaction or heat of our solution. This is going to be equal to our heat of our reaction. So it's gonna be equal to the heat of our reaction. And so now that we have those variables and that's gonna actually be negative because it's going to be the opposite. So now that we have our values, we can go ahead and calculate mass for each. And so if you say the mass of lithium chloride is equal to X, then the mass of our potassium nitrate can be equal to why. And then we can say why is equal to 15 g - whatever the massive X. Is. Because we have 15 g solution. So we're gonna hold on to those variables for now, 4th or 4th step, we're going to calculate our heat and so we have the heat of the reaction Which was equal to negative 1.1587 kg jewels is going to be equal to X. Times are negative 0. that we solved for up here. And then we're gonna add that to our 15 g minus X. Which is our Y. And we're gonna multiply our Y by our 150.3451 kg jule found in step one for our potassium nitrate. Ultimately, when we solve for X, we're going to get that X is equal to 5.2 g. That is going to be for lithium chloride and our why we said it was 15 g minus X. Which is 15 g minus 5.2 g, will give us 9.8 g for potassium nitrate. And with this we have answered our question. So overall, I hope that this helped and until next time

Verified Solution

Key Concepts

Thermochemistry

Specific Heat Capacity

Molar Enthalpy of Solution