Question

What mass of diborane gas, B2H6, occupies 3.48 L at -15°C and 0.454 atm?

B. What is the density of borane gas under these conditions?

C. What is the root-mean-squared speed of borane gas under these conditions?

Answer 1

Part a

Volume of B2H6 V = 3.48 L

Temperature T = - 15 + 273 = 258 K

Pressure P = 0.454 atm

Gas constant R = 0.0821 L-atm/mol-K

PV = nRT

0.454 atm x 3.48 L = n x 0.0821 L-atm/mol-K x 258 K

n = 0.0741 mol

Mass of B2H6 = moles x molecular weight

= (0.0741 mol) x (27.66 g/mol)

= 2.05 g

Part b

Density of B2H6 = mass/volume

= (2.05g) / (3.48L)

= 0.589 g/L x 1L/1000 mL

= 5.89*10^-4 g/mL

Part c

root-mean-squared speed = (3RT/M)^0.5

= (3 x 8314 J/kmol·K x 258K / 27.66 kg/kmol)^0.5

= (2.33 x 10^5)^0.5

= 482.33 m/s