A 5.00-g sample of KBr at 25.0 C dissolves in 25.0 mL of water also at 25.0 C. The final equilibrium temperature of the resulting solution is 18.1 C. What is the enthalpy of solution, delta H (s), of KBr expressed in kilojoules per mole? Last one on prelab got me stumped - Can't figure it out. Thanks for any help
find the moles of KBr ... 5.00 g / molar mass KBr
find energy change ... 25.0 g H2O * specific heat H2O * temperature change H2O
Super
To find the enthalpy of solution, ΔH(s), of KBr, we need to use the equation:
ΔH(s) = q / nKBr
Where ΔH(s) is the enthalpy of solution, q is the heat exchanged between the system and the surroundings, and nKBr is the amount of KBr in moles.
First, let's calculate the heat exchanged, q:
q = mcΔT
Where m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Given:
Mass of KBr (m) = 5.00 g
Volume of water (V) = 25.0 mL = 25.0 g (since 1 mL of water = 1 g)
Initial temperature (T₁) = 25.0°C
Final temperature (T₂) = 18.1°C
Calculate the mass of water:
Mass of water (M) = V = 25.0 g
Calculate the heat exchanged, q:
q = M * c * ΔT
The specific heat capacity of water (c) is 4.18 J/g°C.
ΔT = T₂ - T₁
Substitute the values into the equation to calculate q.
Once you have the value of q, convert it from joules (J) to kilojoules (kJ) by dividing by 1000.
Next, calculate the moles of KBr dissolved:
Moles of KBr (nKBr) = Mass of KBr / molar mass of KBr
The molar mass of KBr is:
K (39.10 g/mol) + Br (79.90 g/mol) = 119.00 g/mol
Substitute the values and calculate nKBr.
Finally, substitute the values of q and nKBr into the equation ΔH(s) = q / nKBr to calculate the enthalpy of solution, ΔH(s), of KBr expressed in kilojoules per mole.
Remember to perform unit conversions as necessary to ensure all units are consistent throughout the calculation.
To determine the enthalpy of solution (ΔH°(s)) of KBr, we can use the equation:
ΔH°(s) = q / n
where:
ΔH°(s) is the enthalpy of solution
q is the heat released or absorbed during the process
n is the amount of KBr in moles
In this case, we need to find the value of q, which represents the heat absorbed or released during the dissolution of KBr.
To do this, we can use the equation:
q = m × c × ΔT
where:
q is the heat transferred
m is the mass of the solvent (water in this case)
c is the specific heat capacity of the solvent
ΔT is the change in temperature
Let's calculate q step by step:
1. Calculate the mass of water (solvent):
The volume of water is given as 25.0 mL. However, specific heat capacity is typically measured in grams, so we need to convert mL to grams. The density of water is 1.0 g/mL, so:
mass = volume × density
mass = 25.0 mL × 1.0 g/mL = 25.0 g
2. Calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
ΔT = 18.1 °C - 25.0 °C = -6.9 °C
Note: The negative sign indicates that heat is being released during the dissolution process.
3. Determine the specific heat capacity (c):
The specific heat capacity of water is approximately 4.184 J/g°C.
4. Calculate q:
q = m × c × ΔT
q = 25.0 g × 4.184 J/g°C × -6.9 °C
Next, we need to convert the obtained q value from joules to kilojoules:
1 J = 0.001 kJ
So, q (kJ) = q (J) × 0.001
Finally, to find the enthalpy of solution (ΔH°(s)), we divide q by the number of moles of KBr:
1. Convert the mass of KBr to moles:
moles of KBr = mass of KBr (g) / molar mass of KBr (g/mol)
The molar mass of KBr is approximately 119 g/mol. Let's perform the calculation:
moles of KBr = 5.00 g / 119 g/mol
2. Substitute the values into the equation:
ΔH°(s) = q (kJ) / moles of KBr
Performing the calculations should give you the enthalpy of solution of KBr expressed in kilojoules per mole.