first-order 2 A(g) → X(g) + 1/2 Y(g) half-life 19.0 min

Consider the hypothetical first-order reaction

2 A(g) → X(g) + 1/2 Y(g)

At a certain temperature, the half-life of the reaction is 19.0 min.

A 1.00-L flask contains A with a partial pressure of 622 mmHg.

If the temperature is kept constant,

what are the partial pressures of A, X, and Y after 42 minutes?

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1차 반응의 반감기

t_1/2 = 0.693 / k

( 참고 https://ywpop.tistory.com/26 )

k = 0.693 / 19.0 min

= 0.03647 /min

Let, certain temperature = 1 K

PV = nRT 로부터,

n / V = P / RT

= (622/760) / 0.08206

= 9.973 M

= [A]_0

1차 반응 속도식

ln([A]_t / [A]_0) = –k•t

[A]_t = e^(–k•t) × [A]_0

= e^(–0.03647×42) × 9.973

= 2.156 M

ICE 도표를 작성하면,

...................... 2 A(g) ..... → ..... X(g) ... + ... 1/2 Y(g)

초기(M): 9.973 ....................... 0 ................... 0

변화(M): –2x .......................... +x .................. +1/2 x

평형(M): 9.973 – 2x .......... x ..................... 1/2 x

[A]_t = 2.156 M 이므로,

[A]_t = 9.973 – 2x = 2.156

2x = 9.973 – 2.156

x = (9.973 – 2.156) / 2

= 3.909 M = X

9.973 – 2x

= 9.973 – 2(3.909)

= 2.155 M = A

3.909 / 2 = 1.955 M = Y

정리하면,

A = 2.155 M

X = 3.909 M

Y = 1.955 M

[참고] 교재 정답에 맞추면,

A = 134 M

X = 244 M

Y = 122 M

A = 134 M 일 때, X는?

2.155 : 3.909 = 134 : ?

? = 3.909 × 134 / 2.155 = 243.1 M

A = 134 M 일 때, Y는?

2.155 : 1.955 = 134 : ?

? = 1.955 × 134 / 2.155 = 121.6 M

[키워드] 1차 반응 기준

first-order 2 A(g) → X(g) + 1/2 Y(g) half-life 19.0 min