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A 100.2 mL sample of 1.00 M NaOH is mixed with 50.1 mL of 1.00 M [tex]H_2SO_4[/tex] in a large Styrofoam coffee cup; the cup is fitted with a lid through which passes a calibrated thermometer. The temperature of each solution before mixing is 22.45°C. After adding the NaOH solution to the coffee cup and stirring the mixed solutions with the thermometer, the maximum temperature measured is 30.90°C. Assume that the density of the mixed solutions is 1.00 g/mL, that the specific heat of the mixed solutions is 4.18 J/(g·°C), and that no heat is lost to the surroundings.

1. Write a balanced chemical equation for the reaction that takes place in the Styrofoam cup. Remember to include phases in the balanced chemical equation.

2. Calculate the enthalpy change per mole of [tex]H_2SO_4[/tex] in the reaction.

Answer :

Answer:

∆H = 95.6 kJ/mol

Explanation:

Step 1: Data given

Volume of a 1.00 M NaOH = 100.2 mL

Volume a 1.00 M H2SO4 = 50.1 mL

The temperature of each solution before mixing is 22.45 °C

The maximum temperature measured is 30.90°C

the density of the mixed solutions is 1.00 g/mL

The specific heat of the mixed solutions is 4.18 J/g°C

Step 2: The balanced equation

2NaOH(aq) + H2SO4(aq) ==> Na2SO4(aq)+ 2H2O(l)


Step 3:

q = mC∆T


⇒q = the heat transfer = TO BE DETERMINED

⇒m = the mass of solution = 100.2 mL + 50.1 mL = 151.2 mL

151.3 ml * 1g/mL = 151.3 grams

⇒c is the specific heat of the solution = 4.18 J/g°C

⇒∆T = the change in temperature = T2 - T1 = 30.90 °C - 22.45 °C = 8.45 °C

q = 151.3 grams * 4.18 Jg°C * 7.65 °C

q = 4838.1 J



Step 4: Calculate ∆H per mole H2SO4


moles H2O4 = 0.0501 L*1.00 M = 0.0501 moles


∆H =4838.1 J / 0.0501 moles = 95569 J/mole = 95.6 kJ/mol

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Rewritten by : Jeany

Final answer:

The balanced chemical equation for the reaction is 2NaOH (aq) + Hâ‚‚SO4(aq) → Naâ‚‚SOâ‚„(aq) + 2Hâ‚‚O(l). To calculate the enthalpy change per mole of Hâ‚‚SO4, use the formula ΔH = q / n and substitute the given values.

Explanation:

The balanced chemical equation for the reaction that takes place in the Styrofoam cup is:

2NaOH (aq) + Hâ‚‚SO4(aq) → Naâ‚‚SOâ‚„(aq) + 2Hâ‚‚O(l)

To calculate the enthalpy change per mole of Hâ‚‚SO4 in the reaction, we need to use the formula:

ΔH = q / n

Where:

  • ΔH is the enthalpy change (in J/mol)
  • q is the heat released or absorbed by the reaction (in J)
  • n is the number of moles of the substance undergoing the reaction

First, we need to calculate the heat released by the reaction using the equation:

q = mcΔT

Where:

  • m is the mass of the solution (in g)
  • c is the specific heat capacity of the solution (in J/(g·°C))
  • ΔT is the change in temperature (in °C)

Now, let's substitute the given values into the equations and calculate the enthalpy change per mole of Hâ‚‚SO4 in the reaction.

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