Final answer:
To find the number of particles of P4 reacted to produce 50 grams of PH3, one must first convert grams of PH3 to moles, use the stoichiometry of the reaction to find moles of P4, and then convert that to particles using Avogadro's number. Approximately 2.21 x 10^23 particles of P4 are reacted.
Step-by-step explanation:
The question asks if 50 grams of PH3 (phosphine) are produced, how many particles of P4 (tetraphosphorus) were reacted. To answer this, we first need to use the chemical equation provided:
P4 + 6 H2 → 4 PH3
This implies that 1 mole of P4 produces 4 moles of PH3. We now calculate the number of moles of PH3 produced from the 50 grams:
Molar mass of PH3 = (1 P x 30.97 g/mol) + (3 H x 1.008 g/mol)
= 34 g/mol
Number of moles of PH3 = 50 grams PH3 / 34 g/mol
= 1.47 moles PH3
Using the stoichiometry of the chemical equation, we determine the moles of P4 reacted:
Given the ratio is 1:4 (P4:PH3),
Number of moles of P4 = 1.47 moles PH3 / 4
= 0.368 moles P4
Since we want to determine the number of particles of P4, we use Avogadro's number (6.022 x 10^23 particles/mol). Thus:
Particles of P4 = 0.368 moles P4 x 6.022 x 10^23 particles/mol
Particles of P4 = 2.21 x 10^23 particles
Therefore, approximately 2.21 x 10^23 particles of P4 were reacted to produce 50 grams of PH3.