Consider a first order gas phase decomposition reaction given below:

A(g) → B(g) + C(g) 

The initial pressure of the system before decomposition of A waspt . After lapse of time ‘t’, total pressure of the system increased by x units and became ‘t’ the rate constant k for the reaction is given as _________.

<p>This is a Fill in the blanks Type Question as classified in NCERT Exemplar</p><p>Ans: Correct option B</p><p>Given:&nbsp;&nbsp;</p><p>A (g) → B (g)&nbsp;+ C (g)&nbsp;</p><p>p_i= Initial pressure</p><p> (Time) t = 0</p><p>&nbsp;</p><p>A (g)&nbsp;→&nbsp;B (g)&nbsp;+ C (g)&nbsp;</p><p>p_{i&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}→0atm&nbsp;+&nbsp;0atm</p><p>t, (p_i&nbsp;- x)atm</p><p>p_t&nbsp;= (p_i&nbsp;- x)atm&nbsp;+ x + x =&nbsp;p_i&nbsp;+ x</p><p>p_A&nbsp;= (p_i&nbsp;- x)</p><p>&nbsp;</p><p>The value of x changes when it is substituted.</p><p>p_A&nbsp;=&nbsp;p_i&nbsp;- (p_t&nbsp;-&nbsp;p_i) = 2p_i&nbsp;-&nbsp;p_t</p><p>K =&nbsp; <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2.303</mn> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </mrow> </mfrac> </math> </span>log<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">p</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <msub> <mrow> <mrow> <mi mathvariant="normal">p</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">p</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> </span></p><p>&nbsp;</p>

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