Use Henry's law and the solubilities given below to calculate the total volume of nitrogen and oxygen gas that should bubble out of 1.2L 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 calculate the total volume of nitrogen and oxygen gas that should bubble out of the water, we can use Henry's law. Henry's law states that the equilibrium concentration of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
First, let's calculate the equilibrium concentration of nitrogen and oxygen in the water at 25C using Henry's law. Since the water is initially saturated with nitrogen and oxygen gas at 25C and a total pressure of 1.0atm, the partial pressures of nitrogen and oxygen are also 1.0atm.
Using the solubilities given, we can convert the solubilities from mg/L to mol/L:
Solubility of oxygen gas at 50C = 27.8 mg/L = 27.8 x 10^-3 g/L = 27.8 x 10^-3 / 32 g/mol = 0.86875 mmol/L
Solubility of nitrogen gas at 50C = 14.6 mg/L = 14.6 x 10^-3 g/L = 14.6 x 10^-3 / 28 g/mol = 0.52143 mmol/L
Now, we can use Henry's law equation to calculate the equilibrium concentration of nitrogen and oxygen in the water at 25C:
C_nitrogen = k_nitrogen * P_nitrogen
C_oxygen = k_oxygen * P_oxygen
Where:
C_nitrogen is the equilibrium concentration of nitrogen gas in mol/L
C_oxygen is the equilibrium concentration of oxygen gas in mol/L
k_nitrogen is the Henry's law constant for nitrogen
k_oxygen is the Henry's law constant for oxygen
P_nitrogen is the partial pressure of nitrogen in atm
P_oxygen is the partial pressure of oxygen in atm
Assuming k_nitrogen = k_oxygen = 1, we can calculate the equilibrium concentrations:
C_nitrogen = 1 * 1.0 = 1.0 mmol/L
C_oxygen = 1 * 1.0 = 1.0 mmol/L
Now, let's calculate the total volume of nitrogen and oxygen gas that should bubble out of the water upon warming to 50C.
To use Henry's law again at 50C, we need to calculate the partial pressure of nitrogen and oxygen above the water at 50C. We know that the air above the water contains an oxygen partial pressure of 0.21atm and a nitrogen partial pressure of 0.78atm.
Using Henry's law at 50C, we can calculate the equilibrium concentrations of nitrogen and oxygen in the water at 50C:
C_nitrogen = k_nitrogen * P_nitrogen
C_oxygen = k_oxygen * P_oxygen
Plugging in the values, we have:
C_nitrogen = 1 * 0.78 = 0.78 mmol/L
C_oxygen = 1 * 0.21 = 0.21 mmol/L
Now, we can find the change in the concentration of nitrogen and oxygen from 25C to 50C:
ΔC_nitrogen = C_nitrogen(50C) - C_nitrogen(25C) = 0.78 - 1.0 = -0.22 mmol/L
ΔC_oxygen = C_oxygen(50C) - C_oxygen(25C) = 0.21 - 1.0 = -0.79 mmol/L
Finally, we can calculate the total volume of nitrogen and oxygen gas that should bubble out of the water using the ideal gas law:
V_gas = (ΔC_gas * V_water) / 1000
Where:
V_gas is the volume of the gas in liters
ΔC_gas is the change in the concentration of the gas in mol/L
V_water is the initial volume of water in liters
Plugging in the values, we have:
V_nitrogen = (-0.22 * 1.2) / 1000 = -0.264 L (negative because the gas is bubbling out)
V_oxygen = (-0.79 * 1.2) / 1000 = -0.948 L (negative because the gas is bubbling out)
Therefore, the total volume of nitrogen and oxygen gas that should bubble out of the water upon warming from 25C to 50C is approximately 0.264 liters of nitrogen gas and 0.948 liters of oxygen gas.