If 0.812g of calcium reacts in a coffee-cup calorimeter that contains 400.0g of water/ The initial temperature of the water is 17.9°C, the final temperature is 26.0°C. Calculate the standard molar enthalpy change for this reaction.
To calculate the standard molar enthalpy change for this reaction, we need to use the equation q = mcΔT. Here's how you can calculate it step-by-step:
Step 1: Calculate the heat gained by the water.
The specific heat capacity of water is about 4.18 J/g°C.
The change in temperature is ΔT = 26.0°C - 17.9°C = 8.1°C.
The mass of the water is 400.0g.
q = mcΔT
q = (400.0g)(4.18 J/g°C)(8.1°C)
q = 13527.6 J
Step 2: Convert the heat to moles of calcium.
The molar mass of calcium (Ca) is 40.08 g/mol.
The mass of calcium used is 0.812g.
moles of Ca = mass of Ca / molar mass of Ca
moles of Ca = 0.812g / 40.08 g/mol
moles of Ca = 0.0202 mol
Step 3: Calculate the standard molar enthalpy change.
The standard molar enthalpy change (∆H) is given by the equation:
∆H = q / moles of Ca
∆H = 13527.6 J / 0.0202 mol
∆H = 668936.6 J/mol
So, the standard molar enthalpy change (∆H) for this reaction is approximately 668936.6 J/mol.
To calculate the standard molar enthalpy change for a reaction, we need to use the equation:
q = m × c × ΔT
Where:
q is the heat absorbed or released by the system (in this case, the water),
m is the mass of the water in grams,
c is the specific heat capacity of water (4.18 J/g°C), and
ΔT is the change in temperature in degrees Celsius.
First, let's calculate the heat absorbed or released by the water using the equation above:
q = (m × c × ΔT)
m = 400.0g (mass of water)
c = 4.18 J/g°C (specific heat capacity of water)
ΔT = (26.0°C - 17.9°C) = 8.1°C (change in temperature)
q = (400.0g × 4.18 J/g°C × 8.1°C)
q = 13,498.8 J (energy)
Next, we need to calculate the moles of calcium used in the reaction. We can use the molar mass of calcium (40.08 g/mol) to convert the mass of calcium (0.812 g) to moles:
moles of calcium = 0.812 g / 40.08 g/mol
moles of calcium = 0.0202 mol
Now, we can calculate the standard molar enthalpy change (ΔH) using the formula:
ΔH = q / moles of calcium
ΔH = 13,498.8 J / 0.0202 mol
ΔH = 667,217.82 J/mol
Therefore, the standard molar enthalpy change for this reaction is 667,217.82 J/mol.