Determine the temperature change when 18.0 g of the following salt is dissolved in 190. g of water. The specific heat capacity of water is 4.184 J·K-1g-1. The enthalpies of solution in the table are applicable. Do not take the added mass of the salt into account when calculating q for the solution.
dH for KCl: +17.2 kJ/mol
dH for MgBr2: -185.6
Have tried using q= mCdT, but keep getting something wrong... Thanks in advance
A negative enthalpy of solution means that the process of dissolving is exothermic. For MgBr2, the molar mass is 184.1 g/mol so 18 g is 0.098 moles. That would release q = 18.1*10^3 J of heat.
Now use your q = mC dT formula.
dT = q/(mC) = 18.1*10^3 J/(190g*4.184 J·K-1g-1)= 23 C
Is that what you got?
ref:
http://en.wikipedia.org/wiki/Enthalpy_change_of_solution
no I didn't get that, but I was adding both 18g of the salt and 190 g of water for the m used in the equation. I'm still a little confused with the signs...I thought if it is releasing heat then q would be negative? I did manage to get the same value for q I just had it negative instead....
If it releasing heat, q is positive but the enthalpy of solution (dH) is negative
Ok, thanks for your help
Just want to double check...so for KCl, because it is endothermic, my q should then be negative?
Yes
To determine the temperature change when the salt is dissolved in water, we need to calculate the enthalpy change (ΔH) for the process.
The formula you mentioned, q = mCΔT, is used to calculate the heat (q) absorbed or released during a temperature change. However, in this case, we need to consider the enthalpy of the solution, which takes into account energy changes associated with the dissolving process.
The enthalpy change (ΔH) for a solution can be calculated using the equation:
ΔH = (moles of solute) x (enthalpy of solution)
First, we need to determine the moles of solute:
- We are given the mass of the salt, which is 18.0 g.
- To convert this mass to moles, we divide by the molar mass of the salt.
It is important to note that KCl and MgBr2 have different molar masses, so we need to calculate the moles separately for each salt.
For KCl:
- The molar mass of KCl is K (39.10 g/mol) + Cl (35.45 g/mol) = 74.55 g/mol.
- The moles of KCl = (mass of KCl) / (molar mass of KCl) = 18.0 g / 74.55 g/mol.
For MgBr2:
- The molar mass of MgBr2 is Mg (24.31 g/mol) + Br (2 x 79.90 g/mol) = 184.31 g/mol.
- The moles of MgBr2 = (mass of MgBr2) / (molar mass of MgBr2) = 18.0 g / 184.31 g/mol.
Now, we can calculate the enthalpy change (ΔH):
- For KCl: ΔH = (moles of KCl) x (enthalpy of solution for KCl) = [(18.0 g / 74.55 g/mol) x (17.2 kJ/mol)]
- For MgBr2: ΔH = (moles of MgBr2) x (enthalpy of solution for MgBr2) = [(18.0 g / 184.31 g/mol) x (-185.6 kJ/mol)]
After obtaining the enthalpy change (ΔH), we can calculate the temperature change (ΔT):
- Using the equation q = mCΔT, we can rearrange it to ΔT = q / (mC), where q is the enthalpy change (ΔH), m is the mass of the solvent (water), and C is the specific heat capacity of water.
Given:
- The mass of water is 190.0 g.
- The specific heat capacity of water is 4.184 J·K-1g-1.
For the KCl solution: ΔT = [ΔH / (m x C)] = [ΔH / (190.0 g x 4.184 J·K-1g-1)]
For the MgBr2 solution: ΔT = [ΔH / (m x C)] = [ΔH / (190.0 g x 4.184 J·K-1g-1)]
Solving for ΔT for each solution will give you the temperature change when the salt is dissolved in water.