What will be the final temperature of the solution in a coffee cup calorimeter if a 50.00 mL sample of 0.250 M HCl(aq) is added to a 50.00 mL sample of 0.250 NaOH(aq). The initial temperature is 19.50 degrees C and the
In order to calculate the final temperature of the solution in the coffee cup calorimeter, we need to use the principle of energy conservation and the equation for heat transfer.
The equation for heat transfer is q = m * c * ΔT, where q represents the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
For this problem, we need to consider the following:
1. The heat transferred from the HCl solution:
q1 = m1 * c1 * ΔT1
2. The heat transferred from the NaOH solution:
q2 = m2 * c2 * ΔT2
3. The total heat transferred equals zero (since there is no heat transfer to or from the surroundings) and is given by:
q1 + q2 = 0
m1 * c1 * ΔT1 + m2 * c2 * ΔT2 = 0
We are given the following information:
- The volume of both solutions is 50.00 mL, which is equivalent to 50.00 g (assuming the density of water).
- The molarity of both solutions is 0.250 M, which means that there are 0.250 moles of solute per liter of solution.
- For a 50.00 mL or 50.00 g solution, the number of moles is:
moles = Molarity * Volume / 1000
moles of solute = 0.250 M * 50.00 mL / 1000 = 0.0125 moles
- The initial temperature is 19.50 degrees Celsius.
Now, let's calculate the heat transferred by each solution and the final temperature of the mixture.
From the equation q1 + q2 = 0, we can rearrange and solve for ΔT2:
ΔT2 = - (m1 * c1 * ΔT1) / (m2 * c2)
Plugging in the values:
ΔT2 = - (50.00 g * 4.18 J/g°C * (19.50°C - 25.00°C)) / (50.00 g * 4.18 J/g°C)
Simplifying:
ΔT2 = - (50.00 g * 4.18 J/g°C * (-5.50°C)) / (50.00 g * 4.18 J/g°C)
Cancelling out similar terms:
ΔT2 = 5.50°C
Now, to find the final temperature, we add the change in temperature ΔT2 to the initial temperature:
Final temperature = Initial temperature + ΔT2
Final temperature = 19.50°C + 5.50°C
Therefore, the final temperature of the solution in the coffee cup calorimeter is 25.00°C.
To find the final temperature of the solution in a coffee cup calorimeter, we can use the principle of conservation of energy and apply the equation for heat transfer:
q = mcΔT
where:
q is the heat transfer
m is the mass of the solution
c is the specific heat capacity of the solution
ΔT is the change in temperature
In this case, we have a 50.00 mL sample of 0.250 M HCl(aq) and a 50.00 mL sample of 0.250 M NaOH(aq).
First, let's calculate the moles of HCl and NaOH:
moles of HCl = volume (L) x concentration (mol/L)
moles of HCl = 0.050 L x 0.250 mol/L = 0.0125 mol
moles of NaOH = volume (L) x concentration (mol/L)
moles of NaOH = 0.050 L x 0.250 mol/L = 0.0125 mol
Since the balanced chemical equation for the reaction between HCl and NaOH is:
HCl(aq) + NaOH(aq) -> H2O(l) + NaCl(aq)
we can see that 1 mole of HCl reacts with 1 mole of NaOH to produce 1 mole of water.
Therefore, the limiting reactant is either HCl or NaOH since they have equal amounts of moles. In this case, let's assume HCl is the limiting reactant.
The reaction between HCl and NaOH is an exothermic reaction, meaning it releases heat. The heat released by the reaction can be calculated using the equation:
q = moles of HCl x ΔH
where:
q is the heat transfer
moles of HCl is the number of moles of HCl
ΔH is the enthalpy change of the reaction
Since the reaction is an exothermic reaction, the ΔH value is negative.
Now, let's assume the specific heat capacity (c) of the solution is 4.18 J/g°C. We can convert the mass of the solution to grams by using the density of water, which is approximately 1 g/mL.
mass of the solution = volume of the solution x density of water
mass of the solution = (50 mL HCl + 50 mL NaOH) x 1 g/mL = 100 g
Now, we can calculate the heat transfer (q) using the equation:
q = mcΔT
Let's assume the final temperature is T (°C), and the initial temperature is 19.50 °C.
q = (100 g) x (4.18 J/g°C) x (T - 19.50 °C)
Since the heat released by the reaction is equal to the heat absorbed by the solution, we can equate the two equations:
q = -moles of HCl x ΔH
By setting -moles of HCl x ΔH equal to mcΔT, we can solve for T:
-moles of HCl x ΔH = (100 g) x (4.18 J/g°C) x (T - 19.50 °C)
Substituting the given values, we have:
- 0.0125 mol x ΔH = 418 J/°C x (T - 19.50 °C)
To find the final temperature (T), we need to know the ΔH value for the reaction between HCl and NaOH. The ΔH value can be obtained from experiment or reference data.
Once we have the ΔH value, we can rearrange the equation and solve for T.