Magnesium m#etal has ΔHfusion = 9.037 kJ>mol and ΔSfusion = 9.79 J>1K mol2. What is the melting point of magnesium in °C? (LO 11.4) (a) 0.923 °C (b) 923 °C (c) 650 °C (d) 1.08 * 103 °C

Video transcript

hi everyone for this problem. It reads the entropy of fusion and entropy of fusion of copper metal are 12.93 Killah jewels per mole and 11.92 jewels per mole kelvin respectively, calculate the melting pot of copper metal in degrees Celsius. So the thing we want to answer here is the melting point of copper and we want to report it in degrees Celsius. And in this problem we're given the entropy of fusion and entropy of fusion. To solve this problem, we're going to want to reference Gibbs free energy change and gibbs free energy changes written out as gibbs free energy change is equal to change in entropy minus temperature times. Change an entropy. Okay. And we want to calculate the melting point of copper and so this is a phase change which means that reaction is at equilibrium. And if the reaction is at equilibrium gives free energy delta G. Is going to equal zero. So what we're going to have is zero is equal to the entropy change of or the entropy of fusion. So yes, we'll write that the entropy of fusion minus temperature times the entropy of fusion. Okay, so let's go ahead because this is set equal to zero. Let's go ahead and move our temperature times the entropy of fusion to the other side. So when we move this to this side, what we get is temperature times entropy of fusion is equal to entropy of fusion. Okay. And we want to isolate temperature. Okay, so we want to isolate temperature. And so what we're gonna do is we're going to divide both sides by entropy of fusion. And so we're going to get temperature which is going to be our melting because we're calculating the melting so we can go ahead and write temperature melting is equal to the entropy of fusion divided by the entropy of fusion. And both of these values we were given in the problem. So all we need to do now is plug those values in. Okay so for our entropy of fusion, the value that we're given is 12.93. Killah jewels per mole. But as you can see we have one unit in killing joules per mole and the other unit and jewels per mole kelvin. So we need both of these temperatures or excuse me we need both of these units to match. So let's go ahead and convert our anthem P. A. Fusion. So we have 12.93 kila jules per mole. Let's go ahead and convert this to jules per mole. Alright so in one kg jule There is 1000 jewels. And our units of kila jules cancel and we're left in jewels per mole. So we're gonna take 12.93 and multiply that by 1000 And when we do that we get 12, jules Permal. So that's the um that is the Value we're going to use for our entropy of fusion. Okay so 12, jewels per mole. And this is going to be over our entropy of fusion which is 11.92 jules over more times kelvin. So that value is also given. So as you can see here our jewels per mole cancel. So we have jewels, mole, jules, mole. So the unit that will be left with when we do this calculation is kelvin which is perfect because kelvin is a temperature unit. So let's go ahead and do this calculation 12,930 divided by 11.92. And the temperature we're going to get in Kelvin is 1000 Excuse me. The temperature we're going to get is 1000 . 7315 for for kelvin. Okay, so this is the temperature in kelvin but the problem asks us to calculate the melting of copper in degrees Celsius. So we need to go from kelvin to degrees Celsius. So what this means is we're going to take our temperature in Kelvin. So 1084. Calvin. And to go from Calvin 2°C we're going to subtract 273.15. Okay, so that means our melting point in degrees Celsius is going to equal 811.6 degrees Celsius. So this is going to be our answer. So out of the multiple choice options given we see that answer. Choice B is going to be the correct answer. Okay, so this is the melting point of copper metal in degrees Celsius. Given the entropy of fusion and entropy of fusion, that is it. For this problem, I hope this was helpful.