A gaseous reaction 3A = 2B is carried out in a 0.0821L closed container initially containing 1 mole of gas A.After sufficient time a curve p (atm) vs T(K) is plotted and the angle with x-axis was found to be 42.95. The degree of association of gas A is(given : tan42.95=0.8)? (a) 0.4 (b) 0.6 (c) 0.5 (d) 0.8?

Question

Answer

The given gaseous reaction is 3A = 2B, where A and B are gases. Initially, the closed container contains 1 mole of gas A.

To determine the degree of association of gas A, we need to analyze the curve p (atm) vs T (K) and find the angle it makes with the x-axis.

Let's break down the problem into smaller steps:

Step 1: Determine the slope of the curve
The slope of the curve can be determined by taking the derivative of the curve equation. However, since the equation is not given, we can estimate the slope by drawing a tangent line at a specific point on the curve. To find the slope, we need to determine the change in pressure (Δp) and the change in temperature (ΔT) at that point.

Step 2: Calculate the tangent of the angle
Using the slope obtained in step 1, we can calculate the tangent of the angle using the formula: tan(angle) = slope. In this case, tan(angle) = 0.8 (given).

Step 3: Calculate the angle
To find the angle, we can take the inverse tangent of the tangent value obtained in step 2. So, angle = arctan(0.8).

Step 4: Calculate the degree of association
The degree of association is related to the stoichiometric coefficients of the reaction. In this case, the ratio of the stoichiometric coefficients is 3:2.

Let's assume that the degree of association is represented by 'x'. This means that after association, the new equation can be written as: (1-x)A = 2B.

Since 1 mole of gas A is initially present, the remaining moles of gas A after association will be (1-x) moles. The moles of gas B formed will be 2x moles.

Step 5: Calculate the ratio of the moles of A and B
The ratio of the moles of A to B can be calculated using the equation: (1-x)/2x = tan(angle).

Substituting the value of tan(angle) (0.8) into the equation, we get: (1-x)/2x = 0.8.

Step 6: Solve for x
Solving the equation from step 5 for x, we can find the value of x, which represents the degree of association of gas A.

Using algebraic manipulation, we get: 1-x = 1.6x.

Simplifying further, we get: 1 = 2.6x.

So, x = 1/2.6 = 0.3846.

Therefore, the degree of association of gas A is approximately 0.4.

Answer: (a) 0.4

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