25.6mL of ethanol (density =0.789 g/mL) initially at 5.4∘C is mixed with 30.4mL of water (density = 1.0 g/mL) initially at 20.4∘C in an insulated beaker.Assuming that no heat is lost, what is the final temperature of the mixture?
heat gained by water + heat lost by ethanol = 0
[mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [mass ethanol x specific heat ethanol x (Tfinal-Tinitial)] = 0.
You will look up the specific heats ethanol and H2O.
To find the final temperature of the mixture, we can use the principle of conservation of energy. This principle states that the heat gained or lost by one substance is equal to the heat lost or gained by the other substance in a system.
In this case, we have two substances, ethanol and water, initially at different temperatures. Since the beaker is insulated, we can assume that there is no heat exchange with the surroundings, and therefore the heat gained by one substance is equal to the heat lost by the other substance.
To find the final temperature, we can use the equation:
q1 + q2 = 0
where q1 is the heat gained or lost by ethanol and q2 is the heat gained or lost by water.
The heat gained or lost by a substance can be calculated using the equation:
q = m * c * ΔT
where q is the heat gained or lost, m is the mass of the substance, c is its specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the mass of ethanol and water:
For ethanol:
Density of ethanol = 0.789 g/mL
Volume of ethanol = 25.6 mL
Mass of ethanol = density * volume = 0.789 g/mL * 25.6 mL = 20.1984 g
For water:
Density of water = 1.0 g/mL
Volume of water = 30.4 mL
Mass of water = density * volume = 1.0 g/mL * 30.4 mL = 30.4 g
Now, let's calculate the heat gained or lost by ethanol and water:
For ethanol:
q1 = m1 * c1 * ΔT1
q1 = 20.1984 g * specific heat capacity of ethanol * (final temperature - 5.4°C)
For water:
q2 = m2 * c2 * ΔT2
q2 = 30.4 g * specific heat capacity of water * (final temperature - 20.4°C)
Since q1 + q2 = 0, we can set up the equation:
m1 * c1 * ΔT1 + m2 * c2 * ΔT2 = 0
Plugging in the values, we can solve for the final temperature:
20.1984 g * specific heat capacity of ethanol * (final temperature - 5.4°C) + 30.4 g * specific heat capacity of water * (final temperature - 20.4°C) = 0
Solving this equation will give us the final temperature of the mixture. However, you need to provide the specific heat capacities of ethanol and water in order to calculate the final temperature accurately.