The air in a hot-air balloon at 735 torr is heated from 22.0°C to 46.0°C. Assuming that the moles of air and the pressure remain constant, what is the density of the air at each temperature? (The average molar mass of air is 29.0 g/mol.)

D1 = 1.16 g/L

D2 = 1.07 g/L

Explanation:

PV = mRT/M

PVM = mRT

PM/RT = m/V = D  - density

D = PM/RT

P = 735 torr

T1= 22.0°C+ 273.15 =  295.15 K

T2 = 46.0°C+ 273.15 =  319.15 K

M = 29.0 g/mol

R = 62.363 torr*L/mol*K

D1 = PM/RT1

D1 = (735 torr*29.0 g/mol) / (62.363 torr*L/mol*K *295.15 K) = 1.16 g/L

D1 = 1.16 g/L

D2 = PM/RT2

D2 = (735 torr*29.0 g/mol) / (62.363 torr*L/mol*K *319.15 K) = 1.07 g/L

D2 = 1.07 g/L

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.