Solar-grade silicon can be manufactured by thermal decomposition of silane at moderate pressure in a fluidized-bed reactor, in which the overall reaction is: SiH4(g) → Si(s) + 2H2(g)When pure silane is preheated to 300°C, and heat is added to the reactor to promote a reasonable

Question

Solar-grade silicon can be manufactured by thermal decomposition of silane at moderate pressure in a fluidized-bed reactor, in which the overall reaction is:

[latex]SiH_{4}(g) → Si(s) + 2 H_{2} (g)[/latex]

When pure silane is preheated to 300°C, and heat is added to the reactor to promote a reasonable reaction rate, 80% of the silane is converted to silicon and the products leave the reactor at 750°C. How much heat must be added to the reactor for each kilogram of silicon produced?

Accepted Answer

For a continuous-flow process with no shaft work and negligible changes in kinetic and potential energy, the energy balance is simply Q = ΔH, and the heat added is the enthalpy change from reactant at 300°C to products at 750°C. A convenient path for calculation of the enthalpy change is to (1) cool the reactant to 298.15 K, (2) carry out the reaction at 298.15 K, and (3) heat the products to 750°C.

On the basis of [latex]1 mol SiH_{4}, the products consist of 0.2 mol SiH_{4}, 0.8 mo l Si, and 1.6 mol H_{2}[/latex]. Thus, for the three steps we have:

[latex] \Delta H_{1} = \int_{573.15K}^{298.15K}{C^{o}_{P}(SiH_{4} )dT }[/latex]

[latex]\Delta H_{2}= 0.8  imes \Delta H^{o}_{298} [/latex]

[latex] \Delta H_{3} = \int_{298.15K}^{1023.15K}{\left[0.2 imes C^{o}_{P} (SiH_{4}) +0.8 imes C^{0}_{P} (Si) + 1.6 imes C^{0}_{P}(H_{2} ) ight]dt}[/latex]

Data needed for this example are not included in App. C, but are readily obtained from the NIST Chemistry WebBook (http://webbook.nist.gov). The reaction here is the reverse of the formation reaction for silane, and its standard heat of reaction at 298.15 K is[latex] \Delta H^{o}_{298} = − 34,310 J[/latex]. Thus, the reaction is mildly exothermic.

Heat capacity in the NIST Chemistry WebBook is expressed by the Shomate equation, a polynomial of different form from that used in this text. It includes a T³ term, and is written in terms of T/1000, with T in K:

[latex] C_P^{\circ}=A+B\left(\frac{T}{1000} ight)+C\left(\frac{T}{1000} ight)^2+D\left(\frac{T}{1000} ight)^3+E\left(\frac{T}{1000} ight)^{-2} [/latex]

Formal integration of this equation gives the enthalpy change:

[latex] \Delta H=\int_{T_0}^T C_P^{\circ} d T [/latex]

[latex] \Delta H=1000\left[A\left(\frac{T}{1000} ight)+\frac{B}{2}\left(\frac{T}{1000} ight)^2+\frac{C}{3}\left(\frac{T}{1000} ight)^3+\frac{D}{4}\left(\frac{T}{1000} ight)^4-E\left(\frac{T}{1000} ight)^{-1} ight]_{T_0}^T [/latex]

The first three rows in the accompanying table give parameters, on a molar basis, for [latex]SiH_4 [/latex], crystalline silicon, and hydrogen. The final entry is for the collective products, represented for example by:

A(products) = (0.2) (6.060) + (0.8)(22.817) + (1.6)(33.066) = 72.3712

with corresponding equations for B, C, D, and E.

Species	A	B	C	D	E
[latex]SiH_4[/latex](g)	6.060	139.96	−77.88	16.241	0.1355
Si(s)	22.817	3.8995	−0.08289	0.04211	−0.3541
[latex]H_2[/latex](g)	33.066	−11.363	−0.08289	−2.773	−0.1586
Products	72.3712	12.9308	2.6505	−1.1549	−0.5099

For these parameters, and with T in kelvins, the equation for ΔH yields values in joules. For the three steps making up the solution to this problem, the following results are obtained:

1. Substitution of the parameters for 1 mol of [latex]SiH_4[/latex] into the equation for ΔH leads upon evaluation to: [/latex]ΔH_1 = −14,860 J[/latex].

2. Here, [latex]ΔH_2[/latex]  = (0.8)(− 34,310) = − 27,450 J .

3. Substitution of the parameters for the total product stream into the equation for ΔH leads upon evaluation to: [latex]ΔH_3[/latex] = 58,060 J.

For the three steps the sum is:

ΔH = − 14,860 − 27,450 + 58,060 = 15,750 J

This enthalpy change equals the heat input per mole of [latex]SiH_4[/latex] fed to the reactor. A kilogram of silicon, with a molar mass of 28.09, is 35.60 mol. Producing a kilogram of silicon therefore requires a feed of 35.60/0.8 or 44.50 mol of [latex]SiH_4[/latex]. The heat requirement per kilogram of silicon produced is therefore (15,750)(44.5) = 700,900 J.

Question 4.9: Solar-grade silicon can be manufactured by thermal decomposi...

Related Answered Questions

What is the maximum temperature that can be reached by the combustion of methane with 20% excess air? Both the methane and the air enter the burner at 25°C. ...

Verified Answer:

A dilute solution of glucose enters a continuous fermentation process, where yeast cells convert it to ethanol and carbon dioxide. The aqueous stream entering the reactor is at 25°C and contains 5 wt-% glucose. Assuming this glucose is fully converted to ethanol and carbon dioxide, and that the ...

Verified Answer:

One method for the manufacture of “synthesis gas” (a mixture of CO and H2) is the catalytic reforming of CH4 with steam at high temperature and atmospheric pressure: CH4 (g) + H2 O(g) → CO(g) + 3H2 (g) The only other reaction considered here is the water-gas-shift reaction: ...

Verified Answer:

Calculate the standard heat of the following methanol-synthesis reaction at 800°C: CO(g) + 2 H2 (g) → CH3 OH(g) ...

Verified Answer:

What is the final temperature when heat in the amount of 400 × 10^6 J is added to 11 × 10³ mol of ammonia initially at 530 K in a steady-flow process at 1 bar? ...

Verified Answer:

The parameters listed in Table C.1 of Appendix C require use of Kelvin temperatures in Eq.(4.5). Equations of the same form may also be developed for use with temperatures in °C, but the parameter values are different. The molar heat capacity of methane in the ideal-gas state is given as a ...

Verified Answer:

Calculate the standard heat of reaction at 25°C for the following reaction: 4HCl(g) + O2 (g) → 2 H2 O(g) + 2 Cl2 (g) ...

Verified Answer:

Calculate the heat required to raise the temperature of 1 mol of methane from 260 to 600°C in a steady-flow process at a pressure sufficiently low that the ideal-gas state is a suitable approximation for methane. ...

Verified Answer:

Verified Answer:

Given that the latent heat of vaporization of water at 100°C is 2257 J ⋅ g^−1, estimate the latent heat at 300°C ...

Verified Answer: