Сосуд вместимостью 100 л разделен на две равные части полупроницаемой перегородкой. В одной половине сосуда находится водород массой 2 г, в другой — азот в количестве 1 моль. Определите давление, установившееся по обе стороны перегородки, если она может пропускать только водород. Температура в обоих половинах одинакова и равна 127 °С. Температура остается постоянной.
To solve this problem, we will use the ideal gas law, PV=nRT, where P is pressure, V is volume, n is moles, R is the universal gas constant, and T is temperature. First, we need to calculate the volume of each half of the vessel. Since the vessel is divided into two equal parts, each half has a volume of 50 liters. Next, we need to find the moles of hydrogen and nitrogen in each half. Since the mass of hydrogen is given as 2 grams and the molar mass of hydrogen is 2g/mol, we have 1 mole of hydrogen in the first half. Similarly, the number of moles of nitrogen in the second half is given as 1 mole. Now, we can plug these values into the ideal gas law to solve for the pressure. Rearranging the equation, we get P=(nRT)/V. Substituting the values, we get P=(1 mol x 8.314 J/molK x 127°C)/50 L = 21.736 atm. Therefore, the pressure on both sides of the membrane will be 21.736 atm, given that the membrane is only permeable to hydrogen.
