Use Henry's law and the solubilities given below to calculate the total volume of nitrogen and oxygen gas that should bubble out of 1.5L of water upon warming from 25C to 50C . Assume that the water is initially saturated with nitrogen and oxygen gas at 25C and a total pressure of 1.0atm. Assume that the gas bubbles out at a temperature of 50C. The solubility of oxygen gas at 50C is 27.8mg/L at an oxygen pressure of 1.00atm. The solubility of nitrogen gas at 50C is 14.6mg/L at a nitrogen pressure of 1.00atm. Assume that the air above the water contains an oxygen partial pressure of 0.21atm and a nitrogen partial pressure of 0.78atm.

To solve this problem, we can use Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

First, we need to calculate the mole fraction of oxygen gas (Xo2) and nitrogen gas (Xn2) in the gas phase using the given partial pressures.

Xo2 = Po2 / Ptotal
Xo2 = 0.21atm / 1.0atm
Xo2 = 0.21

Xn2 = Pn2 / Ptotal
Xn2 = 0.78atm / 1.0atm
Xn2 = 0.78

Next, we need to convert the solubilities of oxygen gas and nitrogen gas at 50C to partial pressures using Henry's Law equation:

Po2 = solubility_oxygen * Po2_std
Po2 = 27.8mg/L * 1.00atm / 27.8mg/L
Po2 = 1.00atm

Pn2 = solubility_nitrogen * Pn2_std
Pn2 = 14.6mg/L * 1.00atm / 14.6mg/L
Pn2 = 1.00atm

Now we can use the mole fraction of oxygen and nitrogen in the gas phase to calculate the partial pressures of oxygen and nitrogen gases in the water at 25C using the given initial total pressure (P0) and solubilities (S) at 25C.

Po2_25C = Xo2 * P0
Po2_25C = 0.21 * 1.0atm
Po2_25C = 0.21atm

Pn2_25C = Xn2 * P0
Pn2_25C = 0.78 * 1.0atm
Pn2_25C = 0.78atm

Now we can assume that the total volume of gas in the water doesn't change during warming from 25C to 50C. Therefore, the total gas pressure (P1) at 50C is still 1.0atm.

Using the solubilities at 50C and the calculated partial pressures at 25C, we can determine the total volume of gas that bubbles out of the water.

Vbub = (V_water * (P1 - P_gas_o2_25C - P_gas_n2_25C)) / (S_gas_o2_50C + S_gas_n2_50C)
Vbub = (1.5L * (1.0atm - 0.21atm - 0.78atm)) / (27.8mg/L + 14.6mg/L)
Vbub = (1.5L * -0.99atm) / 42.4mg/L
Vbub = -33.5L / 42.4mg/L

The negative sign indicates that there is no gas bubbling out of the water at the given conditions. So, the total volume of nitrogen and oxygen gas that should bubble out of 1.5L of water upon warming from 25C to 50C is 0L.

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