6. A sample of hydrogen gas is mixed with water vapor. The mixture has a total p

Question

6. A sample of hydrogen gas is mixed with water vapor. The mixture has a total pressure of 755 torr, and the water vapor has a partial pressure of 24 torr. Wha amount (in moles) of hydrogen gas is contained in 1.55 L of this mixture at 298 K2 7. A 32.5 g cube of aluminum initially at 45.8 °C is submerged into 105.3 g of water at 15.4 oC. What is the final temperature of both substances at thermal equilibrium? Assume the aluminum and water samples are thermally isolated from everything else. Cs values for aluminum and water are, 0.903 and 4.18 J/g °C, respectively.

Explanation / Answer

6.

According to Dalton's law of partial pressures,

Ptotal = PH2 + PH2O

755 = PH2 + 25

PH2 = 730 torr

PH2 = 730 / 760 = 0.9605 atm

T = 298 K

V = 1.55 L

R = 0.0821 L.atm.K-1.mol-1

Ideal gas equation,

P V = n R T

n = 0.09605 * 1.55 / ( 0.0821 * 298 )

n = 0.006085 mol

Therefore,

Mass of H2 gas = moles * molar mass = 0.006085 * 2 = 0.0122 g.

7.

Heat = Mass * specific heat * change in temperature

Heat lost by Al + heat gained by H2O = 0

32.5 * 0.903 * ( t2 - 45.8 ) + 105.3 * 4.18 * ( t2 - 15.4 ) =

29.35 t2 - 1344. + 440.2 t2 - 6778.4 = 0

469.55 t2 = 8122.4

t2 = 8122.4 / 469.55

t2 = Final temperature = 17.3 0C

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