5.0 g of NaNO3 is dissolved in 50.0 g of water. The initial temperature of the water was 21 degrees Celsius and the final temperature of the water is 15.7 degrees Celsius.
1)Calculate the heat of solution, DeltaHsolution.
2) calculate the heat of solution, DeltaHsolution, per mole of NaNO3.
To calculate the heat of solution, DeltaHsolution, we can use the equation:
q = mcΔT
where:
q = heat gained or lost by the substance (in this case, the water)
m = mass of the substance (in this case, the water)
c = specific heat capacity of the substance (in this case, the water)
ΔT = change in temperature
1) Calculate the heat of solution, DeltaHsolution:
First, calculate the heat gained or lost by the water using the equation above.
q = mcΔT
m (mass of water) = 50.0 g
c (specific heat capacity of water) = 4.18 J/g°C (assuming the water density is 1 g/mL)
ΔT (change in temperature) = (final temperature) - (initial temperature) = 15.7°C - 21°C = -5.3°C
q = (50.0 g) * (4.18 J/g°C) * (-5.3°C)
q = -1113.7 J (negative value indicates heat lost)
The heat lost by the water is -1113.7 J. Since the heat lost by the water is equal to the heat gained by the NaNO3, DeltaHsolution is also -1113.7 J.
2) Calculate the heat of solution, DeltaHsolution, per mole of NaNO3:
To calculate the heat of solution per mole, we need to know the number of moles of NaNO3.
moles = mass (in grams) / molar mass
mass of NaNO3 = 5.0 g
molar mass of NaNO3 = 85.0 g/mol (22.99 g/mol (Na) + 14.01 g/mol (N) + (3 × 16.00 g/mol) (O))
moles = 5.0 g / 85.0 g/mol
moles = 0.0588 mol
Now, we can divide DeltaHsolution by the number of moles to calculate the heat of solution per mole.
DeltaHsolution per mole = DeltaHsolution / moles
DeltaHsolution per mole = -1113.7 J / 0.0588 mol
DeltaHsolution per mole ≈ -18,971 J/mol
Therefore, the heat of solution, DeltaHsolution, per mole of NaNO3 is approximately -18,971 J/mol.
To calculate the heat of solution (ΔHsolution) for a given amount of NaNO3 dissolved in water, you can use the equation:
ΔHsolution = (mcΔT) / moles
where:
ΔHsolution = heat of solution
m = mass of water in grams
c = specific heat capacity of water
ΔT = change in temperature
moles = number of moles of NaNO3 dissolved
Let's calculate the answers to your questions step by step:
1) Calculate the heat of solution, ΔHsolution:
First, we need to calculate the mass of water by subtracting the mass of NaNO3 from the total mass:
mass of water = mass of solution - mass of NaNO3
mass of water = 50.0 g - 5.0 g = 45.0 g
Next, we need to calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 15.7 °C - 21 °C = -5.3 °C (Note: We use a negative sign because the temperature decreased)
Now, we can substitute the values into the equation:
ΔHsolution = (mcΔT) / moles
However, we haven't been provided with the moles of NaNO3 dissolved. We can calculate the moles of NaNO3 using the formula:
moles = mass / molar mass
The molar mass of NaNO3 is 85.0 g/mol (Na = 22.99 g/mol, N = 14.01 g/mol, O = 16.00 g/mol)
moles = 5.0 g / 85.0 g/mol = 0.0588 mol
Now, we can plug in the values to calculate ΔHsolution:
ΔHsolution = (45.0 g)(4.18 J/g°C)(-5.3 °C) / 0.0588 mol
Using a calculator, we get:
ΔHsolution ≈ -1718 J/mol
So, the heat of solution for this reaction is approximately -1718 J/mol.
2) Calculate the heat of solution, ΔHsolution, per mole of NaNO3:
To calculate the heat of solution per mole of NaNO3, we divide the heat of solution by the number of moles of NaNO3:
ΔHsolution per mole = ΔHsolution / moles
Substituting the values:
ΔHsolution per mole = -1718 J/mol / 0.0588 mol
Using a calculator, we get:
ΔHsolution per mole ≈ -29260 J/mol
Therefore, the heat of solution per mole of NaNO3 is approximately -29260 J/mol.