Arsenic (iii) sulfide sublimes readily, even below its melting point of 320 c. the molecules of the vapor phase are found to effuse through a tiny hole at 0.28 times the rate of effusion of as atoms under the same conditions of temperature and pressure. what is the molecular formula of as(iii) sulfide in the gas phase?

The molecular formula is As4S6

Explanation:

Step 1: Data given

melting point = 320 °C

The molecules of the vapor phase are found to effuse through a tiny hole at 0.28 times the rate of effusion of As

Step 2: Calculate mean square speed of Ar

µAr = √(3RT/MM)

µAr = √((3*8.314*593)/39.948*10^-3)

µAr = 608.48

Step 3: Calculate the mean speed of arsenic (III) sulfide:

µ = 0.28*µAr = 0.28 * 608.48 =170.37 m/s

Step 4: Calculate molar mass of arsenic (III) sulfide:

µ = √((3R*T)/MM)

170.37 m/s = √((3*8.314 kg*m²/s²*mol*K * 593K)/MM)

170.37² =((3*8.314 kg*m²/s²*mol*K * 593K)/MM)

MM = (3*8.314 kg*m²/s²*mol*K * 593K)/(170.37²)

MM =0.5096 kg /mol  = 509.6 g/mom

The empirical formule for As(III) sulfide = As2S3

As2S3 has a molar mass of 246.035 g/mol

Step 5: Calculate molecular formula of As(III) sulfide

n = 509.6 /246.035

n = 2.07 ≈ 2

This means we have to multiply the empirical formule by 2.

The molecular formula is As4S6