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

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