When 20.8 g of calcium chloride, CaCl2, was dissolved in water in a calorimeter, the temperature rose from 25.0°C to 37.1°C. If the heat capacity of the solution and the calorimeter is 1258 J/°C, what is the enthalpy change when 1 mol of calcium chloride dissolves in water? The solution process is the following.
CaCl2(s) Ca2+(aq) + 2 Cl-(aq
1. Convert 20.8 g CaCl2 to moles (Diveide by the formula mass of CaCl2).
2. The heat given off is:
∆H(sln) = (1258 J/°C)(37.1°C - 25.0°C)
3. Divide the answer in step #2 by the answer in #1 to get the joules/mole. This value is negative since the heat is given off.
To determine the enthalpy change when 1 mole of calcium chloride (CaCl2) dissolves in water, we can use the heat capacity of the solution and calorimeter along with the temperature change.
First, let's calculate the heat released by the solution using the formula:
Q = m × C × ΔT
Where:
Q = heat released (in Joules)
m = mass of the solution (in grams)
C = heat capacity of the solution and calorimeter (in J/°C)
ΔT = change in temperature (in °C)
In this case, the mass of the solution is not given directly, but we know that 20.8 g of calcium chloride was dissolved. We can assume that the mass of the solution is equal to the mass of calcium chloride (20.8 g) since the water has a significantly larger mass and its temperature doesn't change significantly.
So, plugging the given values into the equation:
Q = (20.8 g) × (1258 J/°C) × (37.1°C - 25.0°C)
Calculate the value within the parentheses first:
Q = (20.8 g) × (1258 J/°C) × (12.1°C)
Now, we need to convert grams to moles for calcium chloride (CaCl2) to determine the enthalpy change per mole. The molar mass of CaCl2 is 110.98 g/mol.
So, to convert grams to moles:
moles of CaCl2 = (20.8 g) / (110.98 g/mol)
Calculate the moles:
moles of CaCl2 = 0.1871 mol
Now, we can calculate the enthalpy change per mole using the formula:
ΔH = Q / moles of CaCl2
Plug in the calculated values:
ΔH = Q / (0.1871 mol)
Calculate the enthalpy change:
ΔH = (20.8 g) × (1258 J/°C) × (12.1°C) / (0.1871 mol)
Simplify the calculation:
ΔH ≈ 17278 J/mol
Therefore, the enthalpy change when 1 mole of calcium chloride dissolves in water is approximately 17278 J/mol.