How much does the molar enthalpy change when 147g of water cools from 90°C to 17.0°C? The molar heat capacity for water is 75.3 j/k•mol
What is .147kg*75.3j/kgmol*1mol/18g*(90-17) ?
What is .147kg*75.3j/kgmol*1mol/18g*(90-17) ?
To calculate the molar enthalpy change (ΔH) when 147g of water cools from 90°C to 17.0°C, we can break it down into several steps.
Step 1: Calculate the moles of water.
The molar mass of water (H2O) is approximately 18 g/mol.
Moles = Mass / Molar mass
Moles of water = 147 g / 18 g/mol
Step 2: Calculate the temperature change.
ΔT = Final temperature - Initial temperature
ΔT = 17.0°C - 90°C
Step 3: Calculate the molar enthalpy change using the formula:
ΔH = (moles of water) × (molar heat capacity for water) × (ΔT)
ΔH = (moles of water) × (75.3 J/K•mol) × (ΔT)
Now we can plug in the values:
Moles of water = 147 g / 18 g/mol = 8.17 mol
ΔT = 17.0°C - 90°C = -73.0°C
ΔH = (8.17 mol) × (75.3 J/K•mol) × (-73.0°C)
Calculating the value:
ΔH = -47081.59 J
Therefore, the molar enthalpy change when 147g of water cools from 90°C to 17.0°C is approximately -47081.59 J.
To find the molar enthalpy change, we need to use the formula:
ΔH = n * C * ΔT
Where:
ΔH is the molar enthalpy change (in joules, J)
n is the number of moles of substance
C is the molar heat capacity (in J/(K*mol))
ΔT is the temperature change (in Celsius)
First, we need to convert the mass of water to moles.
The molar mass of water (H₂O) is approximately 18 g/mol.
So, to calculate the number of moles, we divide the mass of water by the molar mass:
n = mass / molar mass
n = 147 g / 18 g/mol ≈ 8.17 mol
Next, we can calculate the temperature change:
ΔT = final temperature - initial temperature
ΔT = 17.0°C - 90.0°C = -73.0°C
Now, we can substitute the values into the formula:
ΔH = n * C * ΔT
ΔH = 8.17 mol * 75.3 J/(K*mol) * -73.0°C
To convert ΔT from Celsius to Kelvin, we add 273.15:
ΔT = -73.0°C + 273.15 = 200.15 K
Now, we can calculate the molar enthalpy change:
ΔH = 8.17 mol * 75.3 J/(K*mol) * 200.15 K
By multiplying these values together, we can obtain the molar enthalpy change.