Calculate the theoretical amount of CaCl2 that would be required to change the temperature of 50 mL of water from from temperature 20 degrees Celsius to 45 degrees Celsius. Remember that the heat lost during the dissociation is equal to the heat gained by the 50.0 mL of water. In order to do this, you will need the heat capacity of water. This value is 4.184 J/g-1 and assume that density of water is 1 g/mL.
heat required is q.
q = mass water x specific heat water x delta T. Now all you need is the heat released when a mole of CaCl2 dissolves.
can someone please explain this question more in detail
thank you
To calculate the theoretical amount of CaCl2 required to change the temperature of water, we need to use the equation:
q = mcΔT
where:
q is the heat gained or lost (in this case, the heat gained by water)
m is the mass of water (in grams)
c is the heat capacity of water (in J/g-1°C-1)
ΔT is the change in temperature (in °C)
Given information:
Volume of water (V) = 50 mL = 50 g (since the density of water is 1 g/mL)
Initial temperature (T1) = 20 °C
Final temperature (T2) = 45 °C
Heat capacity of water (c) = 4.184 J/g-1°C-1
Step 1: Calculate the mass of water (m):
Mass (m) = Volume (V) = 50 g
Step 2: Calculate the change in temperature (ΔT):
ΔT = Final temperature (T2) - Initial temperature (T1)
ΔT = 45 °C - 20 °C
ΔT = 25 °C
Step 3: Calculate the heat gained or lost (q):
q = mcΔT
q = 50 g × 4.184 J/g-1°C-1 × 25 °C
q = 5230 J
Step 4: Calculate the moles of CaCl2 required (assuming complete dissociation):
We know that 1 mole of CaCl2 will release 246.38 kJ (or 246,380 J) of heat during its dissociation.
So, the moles of CaCl2 required = q / (246,380 J/mol)
moles of CaCl2 required = 5230 J / 246,380 J/mol
Now, we need to rearrange the equation to solve for the moles of CaCl2 required:
moles of CaCl2 required = (5230 J / 246,380 J/mol) × (1 mol / 1000 kJ)
Simplifying the expression:
moles of CaCl2 required = 0.0212 mol
Therefore, the theoretical amount of CaCl2 required to change the temperature of 50 mL of water from 20°C to 45°C is approximately 0.0212 moles.
To calculate the amount of CaCl2 required to change the temperature of water, we need to use the equation:
q = mcΔT
where,
q is the heat gained or lost
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g°C)
ΔT is the change in temperature (in °C)
In this case, we are assuming the density of water is 1 g/mL, and we have 50 mL of water, so the mass of the water can be calculated as:
mass of water = density of water × volume of water
mass of water = 1 g/mL × 50 mL
mass of water = 50 g
The specific heat capacity of water is given as 4.184 J/g°C. We need to calculate the heat gained or lost during the temperature change, which can be determined by using the equation mentioned earlier.
q = mcΔT
q = (50 g) × (4.184 J/g°C) × (45 - 20) °C
q = 50 g × 4.184 J/g°C × 25 °C
q = 52,300 J
Since the heat lost during the dissociation of CaCl2 is equal to the heat gained by the water, we can set up an equation to find the amount of CaCl2:
q_cl2 = moles of CaCl2 × ΔH_dissociation
where,
q_cl2 is the heat lost during the dissociation of CaCl2 (calculated earlier as 52,300 J)
ΔH_dissociation is the enthalpy change for the dissociation of CaCl2 per mole (given as an internal value)
Solving for moles of CaCl2:
moles of CaCl2 = q_cl2 / ΔH_dissociation
moles of CaCl2 = 52,300 J / ΔH_dissociation
Now, to find the amount of CaCl2 in grams, we'll use the molar mass of CaCl2:
moles of CaCl2 = mass of CaCl2 / molar mass of CaCl2
mass of CaCl2 = moles of CaCl2 × molar mass of CaCl2
Finally, put all the values together to find the amount of CaCl2 required. Substitute the given values for ΔH_dissociation and the molar mass of CaCl2:
mass of CaCl2 = (52,300 J / ΔH_dissociation) × molar mass of CaCl2
To obtain the final answer, you need to know the values of ΔH_dissociation and the molar mass of CaCl2.