A 0.250-g chunk of sodium metal is cautiously dropped into a mixture of 50 g of water and 50 g of ice?

Question

both at 0 Celcius. The reaction is 2Na (s) + 2H2O(l) yields 2NaOH(aq) + H2(g) Triangle H = -368 kJ

Will the ice melt?Assuming that the final mixture has a specific heat capacity of 4.18 J/g x Celcius calculate the final temperature. the enthalpy fusion of ice is 6.02 Kj/mol

Answer 1

Don't get snowed by all of the numbers!

When the Na gets dropped into the ice/water mixture, the reaction happens, and the negative number for deltaH (not triangle H! The symbol delta means change in heat) means that the reaction creates heat. That heat goes into melting the ice... you don't put things into a freezer to put heat into them, right?

Will enough heat be generated to melt ALL of the ice? Not what the question actually asks, but given all of the numbers, maybe that's what the questioner wants to know.

Here's how you go about it: convert the g of Na to moles = 0.01087 mole). Plug that number of moles into the equation for the heat released (remembering that it's 368 kJ for every 2 moles of Na): you should get the answer that 2 kJ of energy are released. Compare the heat released to the amount of heat needed to melt 50g of ice (which is 2.77 moles, so it will take 6.02 kJ/mol*2.77mol = 16.72 kJ to melt all of the ice).

According to my calculations, the 2 kJ of energy released by the Na reaction will not be enough to melt all of the ice. Therefore, the final temperature will be that of an ice/water mixture, which is 0 degreesC.

Answer 2

Dr W has explained the reasoning admirably. The final temperature will be a little below 0 C, because you have made a solution of sodium hydroxide, and solutions have a lower freezing point than pure solvents.

Are you sure there isn't a typo? If you had 2.50 g Na, there would be enough heat to melt tthe ice, and a little left over to warm the resulting 102.5 g solution by an amount you can calculate using

heat = specific heat x amount x temperature change