When 1.50 g of magnesium metal is allowed to react with 200 mL of 6.00 M aqueous HCl, the temperature rises from 25.0 °C to 42.9 °C. Calculate ΔH in kilojoules for the reaction, assumign that the heat capacity of the calorimeter is 776 J/°C, that the specific heat of the final soltuion is the same as that of water [4.18 J(g·°C)] and that the density of the solution is 1.00 g/mL

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Welcome back everyone. We're told that the temperature increases from 24.9 degrees Celsius to 43.6 degrees Celsius When 1.25 g of calcium metal is allowed to react with mL of 5.50 molar hydrochloric acid. If the heat capacity of the calorie meter is 769 joules divided by graham's degrees Celsius. Its specific heat of the final solution is 4.18 jules divided by grams times degree Celsius and the density of the solution is one g per middle leader. What is the entropy change in kila jewels for the reaction? Our first step is to write out our reaction, we have calcium metal reacting with hydrochloric acid to produce calcium dye bromide as a product which is Aquarius according to our Celje bility rules. And hydrogen gas as our second product. Now to make sure that we have things bounced because we see we have two moles of bromine on the product side, we need to place the coefficient of two in front of our hydrochloric acid, meaning that now we have a balanced equation. And so we're going to use this bounce equation to first calculate our initial moles of each of our reactant so that we can figure out our limiting reactant which is ultimately going to tell us the amount of heat evolved per mole of that reactant based on our entropy change for the reaction. Since we know that entropy change involves an exchange of heat in our reaction. And so that is why we need to begin by finding this limiting reactant. So we're going to find first our initial moles of each of our reactant. So beginning with our calcium, we're going to use that mass given in the prompt for calcium being 1.25 g of calcium. Where we're going to recall from our periodic table the molar mass of calcium equal to 40.0 78 g for one mole of calcium, canceling out our grams of calcium. Leaving us with moles. This is going to yield a total of 0.31189 moles of calcium. Now moving into our moles, our initial moles of hydrochloric acid, our second reactant. We're going to use that volume given the prompt of 150 ml to convert from ml, two leaders and then from leaders into moles. And so we're going to go from leaders to moles because we're going to take that molar concentration for hydrochloric acid given in the prompts in terms of polarity which we should recall can be interpreted as equivalent to moles per liter. And so going back to our story geometry, we have our prefix milli which tells us that we have for one leader 10 to the third power of our male leaders, canceling out milliliters. And now going from our molar concentration of 5.50 moles per liter of our hydroponic acid. We can now cancel out leaders leaving us with moles of hydrochloric acid. And this is going to give us are moles of hydrochloric acid equal to 0.8 to five moles of H. B. R. Initially, now that we have our initial moles of each substance, we need to figure out which is the limiting reactant, which is where we're going to use our coefficients from our balanced equation. And so taking the initial moles of calcium 0.31189 moles of calcium. We're going to multiply it by the molar ratio between moles of calcium and moles of our Prius product, calcium bromide. And so we would see from our coefficients that we have a 1 to 1 molar ratio between calcium and our product and our acquis product. So plugging that 1 to 1 molar ratio in, we can cancel out moles of calcium leaving us with molds of our product. And this is going to yield the exact amount that we started with calcium being 0.31189 moles of calcium. And since we see that we produce the exact amount of, I'm sorry calcium dye bromide that is produced. And since we see that the amount of this product produced is the same as the amount of our Calcium. Initially we know that calcium is likely going to be the limiting reactant. But we can confirm that by carrying on our calculation with the initial moles of hydrochloric acid, which we just calculated at 0.8-5 moles of hydrochloric acid and multiplying it by the molar ratio between moles of H. B. R. And moles of calcium bromide. We see from our balanced reaction that we have a 2 to 1 molar ratio. So we have two moles of hydrochloric acid for one mole of calcium bromide, canceling out our moles of hydrochloric acid leaving us with molds of our product. This gives us our moles of product equal to 0.4125 moles of calcium dye bromide. And so taking the difference between our initial moles of hydrochloric acid .825 moles of H. b. r. From the amount of product produced being How much react. So we would say .4125 moles of hydrochloric acid that is reacted. This difference gives us an excess of hbr being half of our initial amount of 0.4125 moles. And so we would have 0.4125 moles left of our hydroponic acid, meaning that it's an excess and therefore calcium, we can confirm is definitely our limiting reactant. So now that we know are limiting reactant, we're now going to go into our formula to calculate the heat of our reaction which will ultimately give us our entropy change of this heat in the reaction, recall that this is equivalent and let's use a different color here. So for heat of our reaction Q. We have that that is equal to the heat of our calorie emitter. We want to recall plus the heat of our solution. And so what this means is that we're taking the heat of our reaction and calculating it by using our specific heat times. Sorry, our specific heat of our calorie emitter times the difference in temperature experienced by the calorie meter added to the mass of our solution in total, multiplied by the specific heat of our solution, multiplied by delta T. Which is the difference in temperature. And so now we're going to just plug in our units that we know. So what we'll have is that for our specific heat of our color router calorie meter that is given in the prompt as 769 jules divided by degrees Celsius. This is then multiplied by the change in temperature. Where we begin with our final temperature of our calorie emitter given in the prompt as 43.6°C subtracted from its initial temperature of 24.9°C. And then this is added to our total mass of our solution which we will get from taking. And we'll actually do that calculation here really quick. So for the total mass of our solution we want to recall that we can relate density To mass over volume. So we can say that mass is equal to density times volume. Where we would say that the mass is equal to the density given in the prompt of 1. times And sorry, that's 1.00 g per meal leader Times our volume given in the prompt of 150 ml for our solution. And so this is going to give us our mass of 150 g since we can cancel out milliliters. And so we're going to plug that mass in as first being multiplied by our specific heat of our solution given in the prompt as 4.18 joules divided by grams times degrees Celsius multiplied by the mass we just found of 150 g for our solution Which is then multiplied by the difference in temperatures experienced being 43.6°C subtracted from 24.9°C. And so simplifying everything in our next line. We're going to get that the heat of our reaction is equal to the product of our first two terms, which is going to yield the result of 26,105.2. And that is after we added to the second product of the next three terms. So we would get this result and as far as units we can cancel out our units of Celsius as well as our units of on the other side, we can get rid of gramps as well as Celsius. And so we would be left with jewels as our final unit. So plugging that in as jules we want to recall that. We want our heat of our reaction to be in terms of killing jewels. So we're going to multiply by the conversion factor to go from jewels to kill a jules. Where are prefix kilo tells us that we have 10 to the third power of our base unit jewels, canceling out jules being left with killed jules. We have the heat of our reaction equal to a value of 26. kg jules. And so relating this Permal of heat evolved from our limiting reactant calcium. We would say that the heat evolved in the reaction Per mole of calcium is equal to our heat of our reaction, which we just found as 26.1 kill equals divided by our moles of calcium are limiting reactant, which we determined that would be Present initially as 0. moles of calcium. And this quotient is going to yield a value of He'd evolved being 837 kg joules per mole. And so this would be our heat of our reaction. That has evolved. However, we want to recognize that from the prompt. It states that Our final temperature is 43. meaning that the heat went from our reaction to its container being the walls of the calorie meter. And that means that heat was released from our reaction. And so because heat is released, our entropy change, Delta H is going to be negative. And so for our final answer, we would confirm that our entropy change DELTA H is going to equal negative 837 kg joules per mole of heat that is evolved from our reaction. And this would be our final answer to complete this example. I hope that everything I went through is clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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Key Concepts

Stoichiometry

Calorimetry

Enthalpy Change (ΔH)