1.057 grams of a substance with a molar mass of 385.336 g/mol are dissolved in 249.92. Ther temperature for the system changes from 83.83 to 52.38 degrees C during the mixing. What is the DH(heat of solution) for this process in kJ/mol. Assume that th density of water is 1.00g/mL.
I know that the heat capacity is 4.184 J/gK. I calculated the moles of substance and got 0.0027. I found the change in temperature is -31.45 degrees C. Where do I go from here?
q = mass x specific heat x delta T.
but we have a problem.
1.957 g .......are dissolved in 239.92 (what units and what is it dissolved in). My presumption is water but you need to say that.
IF it is 249.92 g H2O, then
the first equation is what you need.
You have two choices. You may use mass H2O in grams, specific heat is already in J/g and delta T you have. Then q will be J. Divide that by the mols of the substance and divide all that by 1000 to convert to kJ and you will have kJ/mol. Post your work if you get stuck.
Sorry about the units. It is 249.92mL of H20. Since the water is not in grams, what equation should I use?
Sorry my friend Barbie and I are doing are chem h.w. together. We each posted a question and since were using the same computer the last name always stays saved in the page...sorry I forgot to change it. It
The problem gives the density of water as 1.00 g/mL; therefore, 249.92 mL = 249.92 grams water. And in my first reponse I gave you only one choice. I can give you the other one but it is more complicated.
Should I use the mass of water, 249.92g, x 4.184j/gk x -31.45 divided by 1000? I did that and got -32.886.
I'm confused though, where does the 1.057g come into play? Also can my number be negative? Am I supposed to change the temperatures into Kelvin?
You do not need to change T to Kelvin. Since a 1 degree change in C is the same as a 1 degrees change in K, you are taking the difference between two temperatures, so you will get the same answer as a difference whether you use K or C.
Here is the way the problem works. You had so many g of a substance that dissolved in water. The equation I wrote first is the way to determine how much energy was spent in dissolving the substance.
q = massH2O x specific heat H2O x delt T for H2O = ?? Joules of heat (in this case lost since the water got colder).
Take that q in Joules, and do this.
a. divide by the mols of the substance. You have the grams and you have molar mass so you can get the mols. (mols = grams/molar mass). q/mol= the amount of heat lost per mole of the substance. Then divide by 1000 to change to kJ/mol and you have it. The sign for the answer is + since heat was absorbed by the substance (where did the heat come from---from the water, of course. The water got colder because heat was extracted from it to go into the substance for it to dissolve). I hope this helpsl I usually don't go into this much detail.
To calculate the DH (heat of solution) for this process in kJ/mol, you need to use the formula:
DH = (q / n) / 1000
where DH is the heat of solution in kJ/mol, q is the heat transferred in J, and n is the number of moles of the substance.
First, you correctly calculated the number of moles of the substance as 0.0027 mol.
Next, you need to calculate the heat transferred, q. Since the heat capacity is given as 4.184 J/gK, it means that 1 gram of the substance requires 4.184 J of heat to raise its temperature by 1 degree Celsius.
To find the heat transferred, q, you need to calculate the change in temperature and the mass of the substance.
The change in temperature is given as -31.45 degrees C (recall that it is negative because the temperature decreased).
Now, you need to calculate the mass of the substance. You were given that 1.057 grams of the substance were dissolved in 249.92 mL of water. We need to convert the volume from milliliters to grams using the density of water, which is 1.00 g/mL:
Mass of water = Volume of water x Density of water
Mass of water = 249.92 g
To get the mass of the substance, you need to subtract the mass of water from the total mass:
Mass of substance = Total mass - Mass of water
Mass of substance = 1.057 g - 249.92 g
Mass of substance = -248.863 g
Note: The negative sign indicates that the substance was dissolved, so its mass became negative relative to the initial state.
Now that you have the change in temperature (-31.45 degrees C) and the mass of the substance (-248.863 g), you can calculate the heat transferred, q:
q = mass x specific heat capacity x change in temperature
Note: The specific heat capacity is given as 4.184 J/gK.
q = -248.863 g x 4.184 J/gK x -31.45 degrees C
q = 32765.443 J
Now, you can substitute the values into the DH formula to calculate the heat of solution, DH:
DH = (q / n) / 1000
DH = (32765.443 J / 0.0027 mol) / 1000
DH = 12108238.5 J/mol
Finally, convert the DH from J/mol to kJ/mol by dividing by 1000:
DH = 12108238.5 J/mol / 1000
DH = 12108.24 kJ/mol
Therefore, the DH (heat of solution) for this process is 12108.24 kJ/mol.