11.75 ton NH4ClO4 and 2.70 ton Al volume of N2 gas

11.75 ton NH4ClO4 and 2.70 ton Al volume of N2 gas

 

 

The fuel in the buster rockets of the Space Shuttle is constituted of a mixture of ammonium perchlorate, NH4ClO4, and aluminum powder. One of the reactions taking place during taking off is given by

6NH4ClO4(s) + 10Al(s) → 5Al2O3(s) + 3N2(g) + 6HCl(g) + 9H2O(g)

The indication (s) and (g) signify solid and gaseous phase. Suppose that these rockets are loaded with 11.75 tons of ammonium perchlorate and 2.70 tons of aluminum. Calculate the volume of nitrogen gas produced during taking off under normal conditions (0℃ and atmospheric pressure, so that 1 mol of gas corresponds to 22.4 L)

 

 

 

> NH4ClO4의 몰질량 = 117.49 g/mol

> Al의 몰질량 = 26.98 g/mol

 

 

 

11750 kg / (117.49 kg/kmol)

= 100.0085 kmol NH4ClO4

( 참고 https://ywpop.tistory.com/7738 )

 

 

 

2700 kg / (26.98 kg/kmol)

= 100.074 kmol Al

 

 

 

100.0085 kmol NH4ClO4와 반응하는

Al의 몰수를 계산하면,

NH4ClO4 : Al = 6 : 10 = 100.0085 kmol : ? kmol

 

? = 10 × 100.0085 / 6 = 166.68 kmol Al

---> Al은 이만큼 없다, 부족하다?

---> Al = 한계 반응물, NH4ClO4 = 과잉 반응물.

( 참고: 한계 반응물 https://ywpop.tistory.com/3318 )

 

 

 

생성물의 양은 한계 반응물의 양에 의해 결정되므로,

Al : N2 = 10 : 3 = 100.074 kmol : ? kmol

 

? = 3 × 100.074 / 10 = 30.02 kmol N2

 

 

 

0℃, 1 atm에서,

기체 1 mol의 부피 = 22.4 L 이므로,

( 참고 https://ywpop.tistory.com/8321 )

 

30.02 kmol × (22.4 kL / 1 kmol)

= 672.448 kL

= 672448 L

= 6.72×10^5 L N2

 

 

 

답: 6.72×10^5 L

 

 

 

 

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[키워드] 한계 반응물 기준, NH4ClO4 + Al 반응 기준