10.1g of potassium nitrate were dissolved in 50cm^3 of water. the temperature fell by 16 degrees celsius. Determine
(a) the number of moles of potassium nitrate dissolve in 50cm^3 of water.
(b) heat change that would be produced if one mole of potassium Nitrate dissolve completely in 1 dm^3 of water.
specific heat capacity of water. (4.18 J kg ^-1 degrees C^-1
a) mols = grams/molar mass
b) q = mass H2O x specific heat H2O x delta T
That gives you delta H/10.1 and
delta H/mol = delta H/10.1 g x ( molar mass/1 mol) and convert that to kJ/mol
10.1/50= 0.202
To determine the answers to these questions, we can follow a step-by-step approach.
(a) To find the number of moles of potassium nitrate dissolved in 50 cm^3 of water, we need to use the molar mass of potassium nitrate and the concentration formula.
1. Calculate the molar mass of potassium nitrate (KNO3):
- The atomic mass of potassium (K) is 39.10 g/mol.
- The atomic mass of nitrogen (N) is 14.01 g/mol.
- The atomic mass of oxygen (O) is 16.00 g/mol.
Multiply the respective atomic masses by the number of atoms in the formula and add them together:
39.10 g/mol (K) + 14.01 g/mol (N) + (16.00 g/mol (O) x 3) = 101.10 g/mol (KNO3)
2. Calculate the number of moles of potassium nitrate (KNO3):
Moles = Mass (g) / Molar Mass (g/mol)
Moles = 10.1 g / 101.10 g/mol
Moles = 0.100 mol
Therefore, there are 0.100 moles of potassium nitrate dissolved in 50 cm^3 of water.
(b) To find the heat change produced when one mole of potassium nitrate dissolves in 1 dm^3 of water, we need to use the heat capacity formula.
1. Recall the equation for heat change (Q):
Q = mcΔT
Where Q is the heat change, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
2. Rearrange the equation to solve for Q:
Q = mcΔT
Q = 1 mol (molar mass of KNO3) * c * ΔT
3. Calculate the molar mass of potassium nitrate as we did in part (a):
Molar mass of KNO3 = 101.10 g/mol
4. Convert the volume of water from dm^3 to cm^3 (1 dm^3 = 1000 cm^3):
Volume of water = 1 dm^3 * 1000 cm^3/dm^3
Volume of water = 1000 cm^3
5. Calculate the mass of water:
Mass = Volume * Density of water
Density of water = 1 g/cm^3 (approximately)
Mass = 1000 cm^3 * 1 g/cm^3
Mass = 1000 g
6. Calculate the heat change (Q):
Q = m * c * ΔT
Q = 1000 g * 4.18 J/g °C * 16 °C
Q = 66,880 J
Therefore, the heat change produced when one mole of potassium nitrate dissolves completely in 1 dm^3 of water is 66,880 J.