Home
Class 12
CHEMISTRY
Decomposition of X exhibits a rate const...

Decomposition of X exhibits a rate constant of `0.5 mu g //` year. How many years are required for the decomposition of `5mu g` of X into `2.5 mu g` ?

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of how many years are required for the decomposition of 5 micrograms of X into 2.5 micrograms, we follow these steps: ### Step-by-Step Solution: 1. **Identify the Reaction Order**: - We are given the rate constant \( k = 0.5 \, \mu g/year \). - The units of the rate constant suggest that this is a zero-order reaction because the unit of \( k \) is mass per time (i.e., \( \mu g/year \)). 2. **Write the Zero-Order Reaction Equation**: - For a zero-order reaction, the relationship between the initial concentration \( A_0 \), final concentration \( A \), rate constant \( k \), and time \( t \) is given by: \[ A = A_0 - kt \] - Here, \( A_0 = 5 \, \mu g \) (initial amount), \( A = 2.5 \, \mu g \) (final amount), and \( k = 0.5 \, \mu g/year \). 3. **Substitute the Known Values into the Equation**: - Substitute the values into the equation: \[ 2.5 \, \mu g = 5 \, \mu g - (0.5 \, \mu g/year) \cdot t \] 4. **Rearrange the Equation to Solve for Time \( t \)**: - Rearranging gives: \[ 0.5 \, \mu g/year \cdot t = 5 \, \mu g - 2.5 \, \mu g \] \[ 0.5 \, \mu g/year \cdot t = 2.5 \, \mu g \] 5. **Solve for \( t \)**: - Divide both sides by \( 0.5 \, \mu g/year \): \[ t = \frac{2.5 \, \mu g}{0.5 \, \mu g/year} = 5 \, years \] ### Final Answer: The time required for the decomposition of 5 micrograms of X into 2.5 micrograms is **5 years**. ---

To solve the problem of how many years are required for the decomposition of 5 micrograms of X into 2.5 micrograms, we follow these steps: ### Step-by-Step Solution: 1. **Identify the Reaction Order**: - We are given the rate constant \( k = 0.5 \, \mu g/year \). - The units of the rate constant suggest that this is a zero-order reaction because the unit of \( k \) is mass per time (i.e., \( \mu g/year \)). ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • JEE MAIN REVISION TEST 8 (2020)

    VMC MODULES ENGLISH|Exercise CHEMISTRY (SECTION 2)|5 Videos
  • JEE MAIN REVISION TEST 5 (2020)

    VMC MODULES ENGLISH|Exercise CHEMISTRY (SECTION 2)|5 Videos
  • JEE MAIN REVISION TEST- 16

    VMC MODULES ENGLISH|Exercise CHEMISTRY (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

How many grams of carbon dioxide is set free by the decomposition of 20 g of calcium carbonate?

How many moles of oxygen gas can be produced during electricity decomposition of 180 g of water ?

Knowledge Check

  • A first order reaction has a rate constant of 5 xx 10^(-3) s^(-1) . How long will 5.0 g of this reaction take to reduce to 3.0 g ?

    A
    34.07 s
    B
    7.57 s
    C
    10.10 s
    D
    15 g
  • Consider a first order gas phase decomposition reaction given below: A (g) to B(g) +C(g) The initial pressure of the system before decomposition of A was pi. After lapse of time 'T', total pressure of the system increased by x units and became ' p_t '. The rate constant k for the reaction is given as

    A
    `k= ( 2.303 )/(t) "log" ( p i)/(p I - x) `
    B
    `k= ( 2.303 )/(t) "log" ( 2p i)/(p I - x) `
    C
    `k= ( 2.303 )/(t) "log" ( p i)/(p I - p_t) `
    D
    `k= ( 2.303 )/(t) "log" ( p i)/(p i - x) `
  • Consider a first order gas phase decomposition reaction given below: A (g) to B(g) +C(g) The initial pressure of the system before decomposition of A was pi. After lapse of time 'T', total pressure of the system increased by x units and became ' p_t '. The rate constant k for the reaction is given as

    A
    `k= ( 2.303 )/(t) "log" ( p i)/(p I - x) `
    B
    `k= ( 2.303 )/(t) "log" ( 2p i)/(p I - x) `
    C
    `k= ( 2.303 )/(t) "log" ( p i)/(p I - p_t) `
    D
    `k= ( 2.303 )/(t) "log" ( p i)/(p i - x) `
  • Similar Questions

    Explore conceptually related problems

    In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?

    A block having 12 g of an element is placed in a room. This element is a radioactive element with a half-life of 15 years. After how many years will there be just 1.5 g of the element in the box ?

    Substance A_(2)B(g) can undergoes decomposition to form two set of products : If the molar ratio of A_(2)(g) to A(g) is 5 : 3 in a set of product gases, then the energy involved in the decomposition of 1 mole of A_(2)B(g) is :

    Substance A_(2)B(g) can undergoes decomposition to form two set of products : If the molar ratio of A_(2)(g) to A(g) is 5 : 3 in a set of product gases, then the energy involved in the decomposition of 1 mole of A_(2)B(g) is :

    Consider a first order gas phase decomposition reaction given below: A (g) to B(g) +C(g) The initial pressure of the system before decomposition of A was pi. After lapse of time 'T', total pressure of the system increased by x units and became ' p_t '. The rate constant k for the reaction is given as