If 1.55g of ptassiumhydroxide is dissolved in 20ml of water, what is the expected temperature change for water?
To calculate the expected temperature change for water, we need to use the concept of heat capacity. Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius (or 1 Kelvin). The heat capacity of water is approximately 4.18 J/g°C (or 4.18 J/gK).
First, we need to determine the amount of heat energy released or absorbed when 1.55g of potassium hydroxide (KOH) is dissolved in water. This can be calculated using the equation:
q = m × C × ΔT
Where:
q = amount of heat energy (in joules)
m = mass of the substance (in grams)
C = heat capacity of the substance (in J/g°C or J/gK)
ΔT = change in temperature (in °C or K)
In this case, the mass of KOH is 1.55g, and the heat capacity of water (C) is 4.18 J/g°C. Since the temperature change (ΔT) is what we want to determine, we rearrange the equation as:
ΔT = q / (m × C)
Now, we need to find the amount of heat energy released when KOH is dissolved. This can be determined by using the heat of solution of KOH, which is approximately -57.6 kJ/mol.
To convert kJ to J, we multiply by 1000:
-57.6 kJ/mol × 1000 J/kJ = -57,600 J/mol
We also need to know the molar mass of KOH, which is:
K (potassium) = 39.10 g/mol
O (oxygen) = 16.00 g/mol
H (hydrogen) = 1.01 g/mol
Total molar mass of KOH = 39.10 + 16.00 + 1.01 = 56.11 g/mol
Now, we can calculate the moles of KOH dissolved using the given mass:
moles of KOH = mass / molar mass
moles of KOH = 1.55g / 56.11 g/mol
Finally, we can calculate the amount of heat energy released:
heat energy (q) = moles of KOH × heat of solution
heat energy (q) = (1.55g / 56.11 g/mol) × -57,600 J/mol
Substituting the calculated values into the original equation, we have:
ΔT = (-57,600 J/mol) / (1.55g × 4.18 J/g°C)
By evaluating the expression, we can determine the expected temperature change for water.