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7.4.5: Calculations and Discussion

  • Page ID
    424829
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    Please show work and/or address the following questions in your notebook. For all quantitative values, show propagation of error and report values \(\pm\) error appropriately.

    Calculations

    1. Calculate the Calorimeter heat capacity:
      Use the calibration data from combustion of benzoic acid to calculate the heat capacity of your calorimeter (\(C_v\)) in kJ (including bomb and contents, bucket, immersed portion of the thermometer) using Equation \ref{12}. Each calorimeter has a unique \(C_v\). The \(C_v\) of your calorimeter should be a constant, provided you always use the same amount of water in each run and the temperature of the calorimeter components is constant. Hint: Use \(\Delta U_{T_1}\) for benzoic acid and solve for \(C_{v,cal}\). \[\Delta U_{T_1} = m\left(26.436 \; \frac{kJ}{g}\right) + m' \left( 6.876 \; \frac{kJ}{g} \right) = -\Delta T_c \left( C_{v,cal} + m"(C_{\ce{H2O}})\right) \label{12}\]
      where
      • \(C_{\ce{H2O}} = 0.00418 \frac{kJ}{deg \; g}\) (heat capacity of water)
      • m = mass of benzoic acid used
      • m' = mass of nickel chromium fuse wire used
      • m'' = mass of water in the bucket
      • \(\Delta T_c\) = corrected temperature rise
      • \(–26.436 \frac{kJ}{g}\) = heat of combustion of benzoic acid
      • \(–6.876 \frac{kJ}{g}\) = heat of combustion of nickel chromium wire
    2. Calculate the \(\Delta U_{T_1}\) of the carbohydrate:
      Use Equation \ref{13} to calculate the energy released from combustion of the carbohydrate. \[\Delta {U}_{ {T}_1}=-\left[\frac{\left[ {C}_{v, cal}+ {m}^{\prime \prime}\left( C_{\ce{H2O}}\right)\right] \Delta {T}_{ {c}}–6.876 \frac{kJ}{g} {~m}^{\prime}}{ {M}}\right] \label{13}\] where \(M\) is the mass of carbohydrate sample used.
    3. Calculate heat of combustion at constant pressure, \(\Delta H_{298}\). (See introduction to calorimetry section and consider how heat and enthalpy are related when pressure is constant). Compare your result with the literature value (The CRC handbook has a table of heats of combustion).
    4. Draw the structure of the sugar and write a balanced chemical equation for combustion of the sugar in oxygen.
    5. Using the molecular weight and empirical formula of the sugar, calculate the heat of combustion in units of kJ/mol at constant pressure (ZWg1Wd0n7B5XtKOhKvfpIqqKmaZoYkV0P_Ug6A5nDNGe9EduDyxBJLoFwQsUs8ZkYziXlrC9qVe3ymLIktkEKiOX6OdF-86LSA7RiPTltN2aTezto3lmkifK_FqrPuOcZTr7RbzArHwYwiwJj4TIQFf0oiM2A20OnMQKGjY0LlZGDWU1XoQYJg8eTTFeg9KZjIGSApP8EQ), at T1 = 298 K (see Introduction section or the Enthalpy section in Atkins). Compare your result with the literature value (The CRC handbook has a table of heats of combustion).
    6. Using standard enthalpies of formation for \(\ce{CO2}\) gas (–393.5 kJ/mol) and \(\ce{H2O}\) gas (–285.83 kJ/mol) and your experimental value for the enthalpy of combustion (\(\Delta H_{T1}\)), calculate the standard enthalpy of formation of the sugar at 25˚C and 1 atm pressure. For the present work the difference between \(\Delta H_{T1}\) and jjWVgZuFCgaOdL3Zhzx4XBisT7FAuI9jpV-TH79QTWUet6AnvVNfyiJklexP-Z5jXGpC2sXQpuhqWVszDCTgdFmP3-tzoDfr_xatWDV4W1ZHYk4EINBW1o6aF3H9p0W3mIY0v57Hvm5hSC_tB3bki-fBpHS6ifB_jh-RJcwYEMhST8VHv8mkd6EAnos0zqaInYxtKJ0nQw may be neglected.1

    Discussion Questions

    1. Discuss possible sources of uncertainty in this experiment,1 and perform a complete propagation of error analysis.
    2. Ask your lab partner for the identity of, and heat of combustion (\(\Delta H_{T_1}\)) of their carbohydrate. **If there is no other student doing this experiment, your TA will give you data for carbohydrate different than yours.
      • In your notebook, compare the carbohydrate you used to that of your partner. Note how the two carbohydrates differ in the \(\Delta H_{T_1}\) and the chemical structure.
      • Using the chemical structure of each sugar, give a rational explanation for the differences in \( \Delta H_{T_1}\).
    3. At high temperatures in the presence of nitrogen gas (\(\ce{N2}\)) oxygen gas (\(\ce{O2}\)), and water, nitric acid can form. This is why the bomb must be flushed with oxygen gas prior to pressurizing it. If residual air were present in the bomb, nitric acid would be formed during combustion; thus the measured temperature rise would be a result of combustion and the oxidation of (\(\ce{N2}\)).2 Explain how could you experimentally could determine if nitric acid was formed, and then how you could correct for the temperature rise due to formation of nitric acid.

    References

    1. Matthews, G. P. Experimental Physical Chemistry, Oxford University Press, Oxford, 1985, Section 3.1.
    2. Atkins, P. W. Physical Chemistry, 6th Edition, W.H. Freeman and Co., New York, NY, 1997, Chapter 2. (Libretexts Textmap here)

    This page titled 7.4.5: Calculations and Discussion is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Kathryn Haas.

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