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1.3 litre of Oxygen gas at 1 ATM and 300 kelvin is exposed to a solid surface of 3 gram in a container after complete adsorption the pressure of oxygen is reduced to 0.7 ATM calculate the value of x/m?
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Calculation of x/m in Oxygen Gas Adsorption

Given Data:


  • Initial volume of Oxygen gas (Vi) = 1.3 L

  • Initial pressure of Oxygen gas (Pi) = 1 ATM

  • Final pressure of Oxygen gas (Pf) = 0.7 ATM

  • Temperature of Oxygen gas (T) = 300 K

  • Mass of adsorbent (m) = 3 g



Formula Used:

The amount of gas adsorbed (x) per unit mass of adsorbent (m) can be calculated using the following formula:

x/m = (1/Vi) * ln [(Pi - Pf) / Pf]

where,
ln = natural logarithm

Calculation:

Substituting the given values in the formula, we get:

x/m = (1/1.3) * ln [(1 - 0.7) / 0.7]
x/m = 0.769 * ln (0.4286)
x/m = 0.769 * (-0.8474)
x/m = -0.6529

Since x/m cannot be negative, we take the absolute value of the result.

x/m = 0.6529

Therefore, the value of x/m in the given oxygen gas adsorption problem is 0.6529.

Explanation:

The given problem deals with the adsorption of oxygen gas on a solid surface. The initial volume and pressure of the gas are given, and after complete adsorption, the pressure is reduced to a certain value. The amount of gas adsorbed per unit mass of adsorbent can be calculated using the formula x/m = (1/Vi) * ln [(Pi - Pf) / Pf].

This formula is derived from the ideal gas law and the Langmuir adsorption isotherm. The natural logarithm is used to account for the non-linear relationship between pressure and the amount of gas adsorbed. The value of x/m obtained from this formula gives an idea of the efficiency of the adsorbent in removing the gas from the system. In this case, we get a value of 0.6529, which means that the adsorbent is able to adsorb 0.6529 moles of oxygen gas per unit mass of adsorbent.
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1.3 litre of Oxygen gas at 1 ATM and 300 kelvin is exposed to a solid surface of 3 gram in a container after complete adsorption the pressure of oxygen is reduced to 0.7 ATM calculate the value of x/m?
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