When 50.0 mL of 1.0 mol/L hydrochloric acid is neutralized completely by 75.0 mL of 1.0 mol/L sodium hydroxide in a coffee-cup calorimeter, the temperature of the total solution changes from 20.2 to 25.6. Determine the quantity of energy transferred, q, and state whether the reaction was endothermic or exothermic.
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To determine the quantity of energy transferred (q), we can use the equation:
q = m * c * ΔT
Where:
q is the quantity of energy transferred (in Joules),
m is the mass of the solution (in grams),
c is the specific heat capacity of the solution (in J/g·°C), and
ΔT is the change in temperature (in °C).
Let's calculate the mass of the solution using the volumes and concentrations provided:
For the hydrochloric acid solution:
Volume = 50.0 mL = 50.0 cm³
Concentration = 1.0 mol/L
n(HCl) = C * V
n(HCl) = 1.0 mol/L * 50.0 cm³
n(HCl) = 0.050 mol
Molar mass of HCl = 1.007 g/mol + 35.453 g/mol = 36.460 g/mol
Mass of HCl = n(HCl) * Molar mass of HCl
Mass of HCl = 0.050 mol * 36.460 g/mol
Mass of HCl = 1.823 g
For the sodium hydroxide solution:
Volume = 75.0 mL = 75.0 cm³
Concentration = 1.0 mol/L
n(NaOH) = C * V
n(NaOH) = 1.0 mol/L * 75.0 cm³
n(NaOH) = 0.075 mol
Molar mass of NaOH = 22.990 g/mol + 16.000 g/mol + 1.008 g/mol = 39.996 g/mol
Mass of NaOH = n(NaOH) * Molar mass of NaOH
Mass of NaOH = 0.075 mol * 39.996 g/mol
Mass of NaOH = 3.000 g
Now, let's calculate the specific heat capacity of the solution. We'll assume it's the same as water (4.18 J/g·°C):
c = 4.18 J/g·°C
Finally, let's calculate the change in temperature:
ΔT = T(final) - T(initial)
ΔT = 25.6 °C - 20.2 °C
ΔT = 5.4 °C
Now, we can calculate the quantity of energy transferred (q):
q = m * c * ΔT
q = (1.823 g + 3.000 g) * 4.18 J/g·°C * 5.4 °C
q = 9.823 g * 4.18 J/g·°C * 5.4 °C
q = 221.7 J
Therefore, the quantity of energy transferred (q) during the reaction is 221.7 Joules.
Since we obtained a positive value for q, it means that energy was absorbed from the surroundings into the system during the reaction. This indicates that the reaction is endothermic.
To determine the quantity of energy transferred (q) during the reaction, you can use the equation:
q = m × c × ΔT
Where:
q is the quantity of energy transferred (in joules, J)
m is the mass of the solution (in grams, g)
c is the specific heat capacity of the solution (in joules per gram per degree Celsius, J/g°C)
ΔT is the change in temperature of the solution (in degrees Celsius, °C)
First, let's calculate the mass of the solution. Since we are given the volume and concentration of the hydrochloric acid and sodium hydroxide solutions, we can use the formula:
m = V × density
In this case, the density of water is approximately 1 g/mL. Therefore, the mass of the hydrochloric acid solution is:
m(HCl) = V(HCl) × density = 50.0 mL × 1 g/mL = 50.0 g
Similarly, the mass of the sodium hydroxide solution is:
m(NaOH) = V(NaOH) × density = 75.0 mL × 1 g/mL = 75.0 g
Next, let's calculate the total mass of the solution:
m(total) = m(HCl) + m(NaOH) = 50.0 g + 75.0 g = 125.0 g
Since the specific heat capacity of water is approximately c = 4.18 J/g°C, we can now calculate the quantity of energy transferred:
q = m(total) × c × ΔT = 125.0 g × 4.18 J/g°C × (25.6°C - 20.2°C)
Simplifying the equation:
q = 125.0 g × 4.18 J/g°C × 5.4°C = 2857.5 J
So, the quantity of energy transferred (q) during the reaction is 2857.5 joules (J).
To determine whether the reaction was endothermic or exothermic, we can analyze the temperature change. If the temperature increased, it means energy was absorbed from the surroundings and the reaction is endothermic. Conversely, if the temperature decreased, it means energy was released to the surroundings and the reaction is exothermic.
In this case, the temperature of the solution changed from 20.2°C to 25.6°C, indicating an increase in temperature. Therefore, the reaction was endothermic.