?The change in the Gibbs energy of a certain constant-pressure process is found to fit

Suggest a physical interpretation of the dependence of the Gibbs energy on the temperature.

Suggest a physical interpretation of the dependence of the Gibbs energy on the pressure.

Suppose that 2.5 mmol of perfect gas molecules initially occupies \(42 \mathrm{cm}^{3}\) at 300 K and then expands isothermally to \(600 \mathrm{cm}^{3}\). Calculate \(\Delta G\) for the process. Text Transcription: 42cm^3 600cm^3 deltaG

Suppose that 6.0 mmol of perfect gas molecules initially occupies \(52 \mathrm{cm}^{3}\) at 298 K and then expands isothermally to \(122 \mathrm{cm}^{3}\). Calculate \(\Delta G\) for the process. Text Transcription: 52cm^3 122cm^3

The change in the Gibbs energy of a certain constant-pressure process is found to fit the expression \(\Delta G / J=-85.40+36.5(T / \mathrm{K})\). Calculate the value of \(\Delta S\) for the process. Text Transcription: deltaG/J = ?85.40 + 36.5(T/K) deltaS

The change in the Gibbs energy of a certain constant-pressure process is found to fit the expression \(\Delta G / J=-73.1+42.8(T / \mathrm{K})\). Calculate the value of \(\Delta S\) for the process. Text Transcription: deltaG/J = ?73.1 + 42.8(T/K) deltaS

The change in the Gibbs energy of a certain constant-pressure process is found to fit the expression \(\Delta G / J=-85.40+36.5(T / K)\). Use the Gibbs–Helmholtz equation to calculate the value of \(\Delta H\) for the process. Text Transcription: deltaG/J = -85.40 + 36.5(T/K) deltaH

The change in the Gibbs energy of a certain constant-pressure process is found to fit the expression ?G/J = ?73.1 + 42.8(T/K). Use the Gibbs–Helmholtz equation to calculate the value of ?H for the process. Text Transcription: deltaG/J = -73.1 + 42.8(T/K) deltaH

Estimate the change in the Gibbs energy of \(1.0 \mathrm{dm}^{3}\) of liquid octane when the pressure acting on it is increased from 1.0 atm to 100 atm. Given that the mass density of octane is \(0.703 \mathrm{~g} \mathrm{~cm}^{-3}\), determine the change in the molar Gibbs energy. Text Transcription: 1.0dm^3 0.703g cm^-3

Estimate the change in the Gibbs energy of \(100 \mathrm{cm}^{3}\) of water when the pressure acting on it is increased from 100 kPa to 500 kPa. Given that the mass density of water is \(0.997 \mathrm{g} \mathrm{cm}^{-3}\), determine the change in the molar Gibbs energy. Text Transcription: 100cm^3 0.997g cm^-3

The change in the molar volume accompanying fusion of solid \(\mathrm{CO}_{2}\) is \(-1.6 \mathrm{cm}^{3} \mathrm{mol}^{-1}\). Determine the change in the molar Gibbs energy of fusion when the pressure is increased from 1 bar to 1000 bar. Text Transcription: CO_2 -1.6cm^3mol^-1

The change in the molar volume accompanying fusion of solid benzene is \(0.5 \mathrm{cm}^{3} \mathrm{mol}^{-1}\). Determine the change in Gibbs energy of fusion when the pressure is increased from 1 bar to 5000 bar. Text Transcription: 0.5 cm^3mol^-1

Calculate the change in the molar Gibbs energy of a perfect gas when its pressure is increased isothermally from 1.0 atm to 100.0 atm at 298 K.

Calculate the change in the molar Gibbs energy of a perfect gas when its pressure is increased isothermally from 50.0 kPa to 100.0 kPa at 500 K.

(a) By integrating the Gibbs–Helmholtz equation between temperature \(T_{1}\) and \(T_{2}\), and with the assumption that \(\Delta H\) is independent of temperature, show that \(\frac{\Delta G\left(T_{2}\right)}{T_{2}}=\frac{\Delta G\left(T_{1}\right)}{T_{1}}+\Delta H\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right)\) where \(\Delta G(T)\) is the change in Gibbs energy at temperature T. (b) Using values of the standard Gibbs energies and enthalpies of formation from the Resource section, determine \(\Delta_{r} G^{\ominus}\) and \(\Delta_{r} H^{\ominus}\) at 298 K for the reaction \(2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow2 \mathrm{CO}_{2}(\mathrm{g})\). (c) Hence estimate \(\Delta_{r} G^{\ominus}\) at 375 K. Text Transcription: deltaGT(T_2)/T_2=deltaG(T_1)/T_1 = deltaG(1/T_2-1/T_1) CO(g) + O_2(g) rightarrow 2 CO_2(g) delta_rG^ominus delta_rH^ominus delta_rG^ominus

Calculate \(\Delta_{r} G^{\ominus}\) and \(\Delta_{r} H^{\ominus}\) at 298 K for \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\). Then, using the result from Problem P3E.1 (a), estimate \(\Delta_{r} G^{\ominus}\) at 500 K and at 1000 K. Text Transcription: delta_rG^ominus delta_rG^ominus delta_rH^ominus N_2(g) + 3 H_2(g) rightarrow 2 NH_3(g)

At 298 K the standard enthalpy of combustion of sucrose is \(-5797 \mathrm{kJ} \mathrm{mol}{ }^{-1}\) and the standard Gibbs energy of the reaction is \(-6333 \mathrm{kJ} \mathrm{mol}{ }^{-1}\). Estimate the additional non-expansion work that may be obtained by raising the temperature to blood temperature, \(37^{\circ} \mathrm{C}\). (Hint: use the result from Problem P3E.1 to determine\(\Delta_{r} G^{\ominus}\) at the higher temperature.) Text Transcription: -5797 kJ mol^-1 -6333 kJ mol^-1 37 degree C delta_rG^ominus

Consider gases described by the following three equations of state: (a) \(\text { perfect: } p=\frac{R T}{V_{\mathrm{m}}}\) (b) \(\text { van der Waals: } p=\frac{R T}{V_{\mathrm{m}}-b}-\frac{a}{V_{\mathrm{m}}^{2}}\) (c) \(\text { Dieterici: }p=\frac{R T \mathrm{e}^{-a / K T V_{\mathrm{m}}}}{V_{\mathrm{m}}-b}\) Use the Maxwell relation \((\partial S / \partial V)_{T}=(\partial p / \partial T)_{V}\) to derive an expression for \((\partial S / \partial V)_{T}\) for each equation of state. For an isothermal expansion, compare the change in entropy expected for a perfect gas and for a gas obeying the van der Waals equation of state: which has the greatest change in entropy and how can this conclusion be rationalized? Text Transcription: perfect: p = RT/V_m Van der waals: p = RT/v_m-b - a/V^2m dieterici: p = RTe^9/RTV_m/V_m-b (partial_S/partial_V)r = (partial_p/partial_T)r (partial_S/partial_V)r

Only one of the four Maxwell relations is derived in the text. Derive the remaining three to give the complete set listed in Table 3E.1. Start with the definition of H (H = U + pV), form the exact differential (dH = dU + pdV + Vdp), and then substitute dU = TdS ? pdV. The resulting expression gives rise to a Maxwell relation in a way analogous to how eqn 3E.5 arises from eqn 3E.1. Repeat the process, starting with the definitions of A and then G, to give the remaining two Maxwell relations.

Suppose that S is regarded as a function of p and T so that Use \((\partial S / \partial T)_{p}=C_{p} / T\) and an appropriate Maxwell relation to show that \(\mathrm{Td} S=C_{p} \mathrm{d} T-\alpha T V \mathrm{d} p\), where the expansion coefficient, ?, is defined as \(\alpha=(1 / V)(\partial V / \partial T)_{p}\). Hence, show that the energy transferred as heat, q, when the pressure on an incompressible liquid or solid is increased by \(\Delta p\) in a reversible isothermal process is given by \(q=-\alpha T V \Delta p\). Evaluate q when the pressure acting on \(100 \mathrm{cm}^{3}\) of mercury at \(0^{\circ} \mathrm{C}\) is increased by 1.0 kbar. (\(\alpha=1.82 \times10^{-4} \mathrm{K}^{-1}\).) Text Transcription: (partialS/partialT)_p = C_p/T TdS = C_pdT ? alphaTVdp (1/V)(partialV/partialT)_p q = ?alphaTVdeltap. (alpha = 1.82 × 10^?4 K^?1.) 100 cm^3 0 degree C

The pressure dependence of the molar Gibbs energy is given by \(\left(\partial G_{\mathrm{m}} / \partial p\right)_{T}=V_{\mathrm{m}}\). This problem involves exploring this dependence for a gas described by the van der Waals equation of state (a) Consider first the case where only the repulsive term is significant; that it, a = 0, \(b \neq 0\). Rearrange the equation of state into an expression for \(V_{\mathrm{m}}\), substitute it into \(\left(\partial G_{m} / \partial p\right)_{T}=V_{m}\), and then integrate so as to obtain an expression for the pressure dependence of \(G_{m}\). Compare your result with that for a perfect gas. (b) Now consider the case where only the attractive terms are included; that is, b = 0, \(a \neq 0\). The equation of state then becomes a quadratic equation in \(V_{\mathrm{m}}\). Find this equation and solve it for \(V_{\mathrm{m}}\). Approximate the solution by assuming that \(p a / R^{2} T^{2} \ll 1\) and using the expansion \((1-x)^{1 / 2} \approx 1-\frac{1}{2} x\), which is valid for x << 1. Hence find an expression for the pressure dependence of \(G_{m}\), and interpret the result. (c) For \(\mathrm{CO}_{2} a=3.610 \mathrm{atm}\mathrm{dm}^{6} \mathrm{mol}^{-2}\), \(b=4.29 \times 10^{-2} \mathrm{dm}^{3} \mathrm{mol}^{-1}\). Use mathematical software to plot \(G_{m}\) as a function of pressure at 298 K for a perfect gas and the two cases analysed above. (Use \(R=8.2057 \times 10^{-2} \mathrm{dm}^{3} \text { atm } \mathrm{K}^{-1} \mathrm{mol}^{-1}\).) Text transcription: (partialG_m/partialp)_T = V_m b neq 0 a neq 0 (partialG_m/partialp)_T = V_m V_m V_m V_m G_m G_m G_m (1-x)^½ = 1 - 1/2x pa/R^2T^2<<1 CO_2 a = 3.610 atm dm^6 mol^?2 b = 4.29 × 10?2 dm^3 mol^?1 R = 8.2057 × 10^?2 dm3 atm K^?1 mol^?1

Nitric acid hydrates have received much attention as possible catalysts for heterogeneous reactions that bring about the Antarctic ozone hole. Worsnop et al. (Science 259, 71 (1993)) investigated the thermodynamic stability of these hydrates under conditions typical of the polar winter stratosphere. They report thermodynamic data for the sublimation of mono-, di-, and trihydrates to nitric acid and water vapours, \(\mathrm{HNO}_{3} \cdot n \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightarrow\mathrm{HNO}_{3}(\mathrm{g})+n \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\), for n = 1, 2, and 3. Given \(\Delta_{\tau} G^{\ominus}\) and \(\Delta_{\tau} H^{\ominus}\) for these reactions at 220 K, use the Gibbs–Helmholtz equation to compute \(\Delta_{\tau} G^{\ominus}\) for each at 190 K. Text Transcription: HNO_3·nH_2O(s) ? HNO_3(g) + nH_2O(g) delta_rG^ominus delta_rG^ominus delta_rH^ominus