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in States of Matter - Gas and Liquid by (48.1k points)

4.05 ml of phosphorus vapour weighs 0.0625g at 546 °C and 0.1 bar pressure. What is the molar mass of phosphorus?

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Given, P = 0.1 bar
V = 34.05 mL = 34.05 × 10-3L
= 34.05 × 10-3 dm3
R = 0.083 bar dm3K-1mol-1
T = 546°C = (546 + 273) K = 819 K
The number of moles (n) can be calculated using the ideal gas equation as:
From the gas equation
PV = w ,RT/M,we get
M = w. RT/ PV      …(1)
Substituting the given values in the equation (1), we get M = (0.0625 / 0.1 × 34.04) × 82.1 × 819 = 124.75 g/mol
Hence, the molar mass of phosphorus is 124.75 g mol-1.

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