Consider the reaction of Lithium with water:
2 Li(s) + 2H2O(l) ----> 2 LiOH(aq) + H2(g)
The delta H of the reaction is -160 KJ
The enthalpy of fusion of H2O is 6.0 kJ/mol
The specific heat capacity of H2O(l) is 4.18 J/gC
When 10 grams of Li(s) is dropped in a container containing ice and liquid water at 0 degrees Celsius, how many grams of ice will melt?
A) 78.5 g
B) 350 g
C) 19.3 g
D) 700 g
To solve this question, we need to calculate the amount of heat released by the reaction between lithium and water and then determine how much ice will melt as a result of this heat release.
First, let's calculate the heat released by the reaction using the given enthalpy change (ΔH) value of -160 kJ. Since the reaction involves 2 moles of Li reacting with water, we can use the balanced equation to determine the moles of Li reacting:
2 Li(s) + 2H2O(l) → 2 LiOH(aq) + H2(g)
From the equation, we know that 2 moles of Li react to give -160 kJ of energy. Therefore, 1 mole of Li reacts to give -160 kJ / 2 = -80 kJ of energy.
Next, let's determine the mass of lithium used. The molar mass of Li is 6.94 g/mol. We are given that 10 grams of Li is used in the reaction, so the number of moles of Li is:
moles of Li = 10 g / 6.94 g/mol ≈ 1.44 mol
Now, we can determine the total heat released by the reaction:
Heat released by the reaction = moles of Li * energy change per mole
= 1.44 mol * (-80 kJ/mol) ≈ -115.2 kJ
Since the reaction releases heat, it will cause the temperature of the surroundings to increase. In this case, the surroundings consist of the ice and water at 0 degrees Celsius.
The heat released by the reaction will be used to melt some of the ice. The amount of ice that will melt can be calculated using the enthalpy of fusion of water (6.0 kJ/mol) and the specific heat capacity of water (4.18 J/g°C).
The amount of ice melted can be calculated using the equation:
Mass of ice = Heat released by the reaction / (Enthalpy of fusion of water + Specific heat capacity of water * Change in temperature)
Since the temperature remains constant at 0 degrees Celsius during the process of melting ice, the change in temperature will be 0°C. Substituting the given values into the equation:
Mass of ice = -115.2 kJ / (6.0 kJ/mol + (4.18 J/g°C) * 0°C)
= -115.2 kJ / 6.0 kJ/mol ≈ -19.2 mol
Since the molar mass of water is approximately 18 g/mol, the mass of ice melted will be:
Mass of ice = -19.2 mol * 18 g/mol ≈ 346.8 g
Therefore, the closest option to the calculated value is B) 350 g.