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Does the Silence Dust from the Alchemy Manual, prevent the casting of spells with Verbal Components?
For reference:
Silence Dust:
Silence dust
Source: Alchemy Manual pg. 15
Price: 60 gp; Weight: 1 lb.
Category: Alchemical Tools
Description
This ashen powder can be thrown as a splash weapon, muffling all sound within a 15-foot-radius sphere centered on the point of impact. Perception checks to notice sound emanating from or passing through the cloud take a –10 penalty. Alternatively, applying a dose of silence dust to your feet as a standard action grants you a +5 circumstance bonus on Stealth checks to avoid being heard while walking. The dust is effective for 1 minute before it disperses.
Source: Alchemy Manual pg. 15
Price: 60 gp; Weight: 1 lb.
Category: Alchemical Tools
Description
This ashen powder can be thrown as a splash weapon, muffling all sound within a 15-foot-radius sphere centered on the point of impact. Perception checks to notice sound emanating from or passing through the cloud take a –10 penalty. Alternatively, applying a dose of silence dust to your feet as a standard action grants you a +5 circumstance bonus on Stealth checks to avoid being heard while walking. The dust is effective for 1 minute before it disperses.

Lost In Limbo |

I would say no.
Looking at the paragraph on verbal components on page 184 of the Core Rulebook;
Core Rulebook wrote:
To cast a spell with a verbal (V) component, your character must speak in a firm voice. If you’re gagged or in the area of a silence spell, you can’t cast such a spell. A spellcaster who has been deafened has a 20% chance to spoil any spell he tries to cast if that spell has a verbal component.
And looking at the silence spell;
Core Rulebook wrote:
Upon the casting of this spell, complete silence prevails in the affected area. All sound is stopped: Conversation is impossible, spells with verbal components cannot be cast, and no noise whatsoever issues from, enters, or passes through the area.
So the complete silence of the silence spell (or being effectively gagged) makes verbal components, and the spells that they are part of, fail. Silence Dust on the other hand only muffles sound, it doesn't negate it.
At the very most I would give a failure chance similar to if a deafened mage was trying to cast a spell with a verbal component, and probably not even that. It seems too cheap for so strong an effect as crippling almost all spellcasters.