Step 1: Define Disproportionation and Redox Reactions
A disproportionation reaction occurs when a single element is simultaneously oxidized and reduced. A standard redox reaction, conversely, involves the oxidation and reduction of distinct elements.
Step 2: Analyze Oxidation States
Examine the oxidation states of phosphorus (P) and sulfur (S) in the reaction: \[ P_4 + 8SOCl_2 \rightarrow 4PCl_3 + 2S_2Cl_2 + 4SO_2 \] In elemental phosphorus (\( P_4 \)), P has an oxidation state of \( 0 \).
In phosphorus trichloride (\( PCl_3 \)), P has an oxidation state of \( +3 \).
In sulfur oxychloride (\( SOCl_2 \)), S has an oxidation state of \( +4 \).
In disulfur dichloride (\( S_2Cl_2 \)), S has an oxidation state of \( +2 \).
In sulfur dioxide (\( SO_2 \)), S has an oxidation state of \( +4 \).
Step 3: Determine Reaction Type
Phosphorus (\( P \)) is oxidized from \( 0 \) to \( +3 \).
Sulfur (\( S \)) is reduced from \( +4 \) to \( +2 \).
As phosphorus only undergoes oxidation and sulfur only undergoes reduction, this is a simple redox reaction, not a disproportionation reaction.
Step 4: Evaluate Other Options
Option (A) describes a disproportionation reaction because phosphorus is both oxidized and reduced.
Option (B) involves the disproportionation of oxygen, changing from \( -1 \) to \( -2 \) and \( 0 \).
Option (C) also demonstrates the disproportionation of phosphorus.
A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as:
$ x = t^3 - 6t^2 + 20t + 15 $.
The velocity of the body when its acceleration becomes zero is: