The Question is from neet-physics units-and-measurement , and it was created by the author ABDUL JILANI BASHA

Question

A chemist measures a reaction rate as $2.5 	imes 10^{-3}$ mol L$^{-1}$ $s^{-1}$.  Express this rate in molecules $cm^{-3}$ $\mu s^{-1}$ (molecules per cubic centimeter per microsecond). Avogadro's number = $6.022 	imes 10^{23}$ molecules/mol.

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option C]
## CONCEPT FRAMEWORK
	**Primary Concept**: Unit Conversion
	**Related Topics**: Stoichiometry, Avogadro's Number
	**Prerequisites**: Understanding of unit conversions, Avogadro's number, and scientific notation.
## SOLUTION PATHWAY
**Given Information**:
	* Reaction rate = $2.5 	imes 10^{-3}$ mol L$^{-1}$ s$^{-1}$
	* Avogadro's number = $6.022 	imes 10^{23}$ molecules/mol
	* Conversion factors: 1 L = 1000 cm$^3$, 1 s = $10^6$ $\mu$s
**Method & Steps**:
	1. Convert mol to molecules using Avogadro's number.
		Reasoning: The given rate is in moles, which needs to be converted to the number of molecules.
		Formula/Rule:  Number of molecules = moles × Avogadro's number
	2. Convert L$^{-1}$ to cm$^{-3}$.
		Reasoning: We need the volume unit to be in cm$^3$ instead of L.
		Formula/Rule: 1 L = 1000 cm$^3$ or 1 L$^{-1}$ = 1/1000 cm$^{-3}$ = $10^{-3}$ cm$^{-3}$
	3. Convert s$^{-1}$ to $\mu$s$^{-1}$.
		Reasoning: The time unit should be in microseconds.
		Formula/Rule: 1 s = $10^6$ $\mu$s or 1 s$^{-1}$ = $10^{-6}$ $\mu$s$^{-1}$
	4. Multiply all conversion factors with the given rate.
		Working: Rate in molecules cm$^{-3}$ $\mu$s$^{-1}$ = ($2.5 	imes 10^{-3}$ mol L$^{-1}$ s$^{-1}$) × ($6.022 	imes 10^{23}$ molecules/mol) × ($10^{-3}$ L cm$^{-3}$) × ($10^6$ s $\mu$s$^{-1}$)
		Key Point: Ensure all units are cancelling correctly, leaving the desired units.
	5. Calculate the final value
		Result: Rate = $2.5 	imes 6.022 	imes 10^{-3+23-3+6}$ molecules cm$^{-3}$ $\mu$s$^{-1}$ = $15.055 	imes 10^{23-6}$ molecules cm$^{-3}$ $\mu$s$^{-1}$ = $1.5055 	imes 10^{16}$ molecules cm$^{-3}$ $\mu$s$^{-1}$ ≈ $1.5 	imes 10^{15}$ molecules cm$^{-3}$ $\mu$s$^{-1}$
		Verification: The final units are correct, and the numerical value is within reasonable range.
 ## OPTION ANALYSIS
[A] :x: Incorrect calculation.
[B] :x: Incorrect calculation.
[C] ✓: Correct calculation, the value and the units are accurate.
[D] :x: Incorrect calculation.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Incorrect unit conversion (e.g., using incorrect conversion factors or not converting all units).
			[How to avoid]: Double-check each conversion factor and ensure all units cancel correctly.
		2. [Error 2]: Incorrect use of scientific notation.
			[How to avoid]: Pay close attention to the exponents during multiplication and division.
	**Quick Tips**:
		1. [Helpful shortcut]: Write out each conversion step and cancel the units to avoid mistakes.
		2. [Memory aid]:  Remember Avogadro's number and the basic unit conversions for volume (L to cm$^3$) and time (s to $\mu$s).

ABDUL JILANI BASHA · Answer

$1.5 	imes 10^{12}$ molecules $cm^{-3}$ $\mu s^{-1}$

ABDUL JILANI BASHA · Answer

$2.5 	imes 10^{18}$ molecules $cm^{-3}$ $\mu s^{-1}$

ABDUL JILANI BASHA · Answer

The correct Option is "$1.5 	imes 10^{15}$ molecules $cm^{-3}$ $\mu s^{-1}$"

ABDUL JILANI BASHA · Answer

$4.2 	imes 10^{20}$ molecules $cm^{-3}$ $\mu s^{-1}$

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