The Solution of Gas Law Problems MARTIN M E Y E R Brooklyn College, Brooklyn, New York
of general chemistry are required to STUDENTS learn the Ideal Gas Law, but to solve problems they are usually taught to employ some of the expressions derived from it. These expressions, from the student's standpoint, frequently have only the significance of arbitrary formulas. All gas problems of the ordinary elementary types may, of course, be solved directly from the Ideal Gas Law, pv = nRT
Taking v as 22.41 liters, 9 in mm., and evaluating R for one mole of gas a t N.T.P., we have, pu = 62.37nT
For any weight of gas, n may obviously be computed from the chemical formula of the gas. For the reduction of a volume given under any conditions to N.T.P., we first obtain,
Then Y ~ . T . P .=
22.41%liters
The solution is based upon simple geometric and trigonometric principles. DCBA is a portion of a right triangle with the right angle a t B , and the angle or according to the data given is 70°14'. BE may he The calculation involved in (1) (or any similar calcu- drawn a t any angle, but 45O is convenient. Several devices may be learned in using this method. lation) may be done graphically as shown in Figure 1. Using a ruler graduated in mm. and a hand lens to The method may also be carried out by construction, or aid in estimating to tenths, lay off T and fi successively various mechanical models may be built with BC, BE, along BE in mm./lO. Lay off v in mm./lO (or any and B A graduated directly, and mechanical methods convenient fraction) along BC. Draw VT and then for carrying the points across. With a model only 20 P X parallel to it. Draw VY and XZ parallel to AD cm. in its longest dimension results as accurate as those and intersecting B A in Y and 2. Measure the dis- of a cheap slide rule may be obtained, and students find it more interesting. tance YZ in mm./lO. This is ~ x . T . P .
