Chemistry Example

Problem

In a calorimetry experiment, 50.0 mL of 0.200 ± 2% M hydrochloric acid (HCl) at an initial temperature of 25.0°C is added to 50.0 mL of 0.200 ± 2% M sodium hydroxide (NaOH) at an initial temperature of 25.0°C in a polystyrene foam cup calorimeter. The temperature of the solution increases to 31.2°C after the reaction is complete. The specific heat capacity of the solution is assumed to be 4.18 J/g°C. The density of the solution is 1.00 g/mL.

The volume of each of the solutions was measured using a graduated cylinder. The temperature of the solution was measured using a digital sensor probe.

Calculate the change in enthalpy of the reaction (ΔH) in kJ/mol with its uncertainty.

Solution

Balanced Chemical Equation:

\[HCl + NaOH \rightarrow NaCl + H_{2}O\]

Formulas:

\[\Delta T = T_f - T_i\]

\[m = \rho V\]

\[Q = m c \Delta T\]

\[n = M V\]

\[\Delta H = -\frac{Q}{n}\]

>>> molarity = M.fromStr('0.200 +/- 2% mol/mL')
>>> volume = M.fromStr('50.0a mL')
>>> t_i = M.fromStr('25.0d °C')
>>> t_f = M.fromStr('31.2d °C')
>>> density = M.fromStr('1.00c g/mL')
>>> t_change = t_f - t_i
>>> mass = density * volume
>>> q = mass * M.fromFloat(4.18, 'J/(g*°C)') * t_change
>>> n = molarity * volume
>>> delta_h = -q / n
>>> delta_h
-1.3E+2 +/- 7% J/mol

Thus, this reaction has a change in enthalpy of \(-1.3 \times 10^2 \pm 7\%\) J/mol.