The pressure P of a gas in a leak-tight container can be approximated by , where V is the volume of the container, T is its absolute (Kelvin) temperature, and k is a constant. Find and .

Question

The pressure P of a gas in a leak-tight container can be approximated by  , where V is the volume of the container, T is its absolute (Kelvin) temperature, and k is a constant. Find  and  .

Quizplus · Accepted Answer

By comparing the given expression with the ideal gas law PV = nRT, we can see that k = nR, where n is the number of moles of gas and R is the universal gas constant. Therefore, the units of k are J/K. In the given expression, we have P = 11eaa948_cd96_9a26_84bc_7164596dbc78_TB2342_11 , V = V, T = T, and k = 11eaa948_cd96_c137_84bc_3f096d654ecb_TB2342_11 . To find k, we need to rearrange the equation as k = P/(nT/V) = PV/NT. Since N/NA = n, we can write k = (NA/V)RT, where NA is Avogadro's number. Therefore, k = (6.022 × 10^23/V) × 8.314 J/(mol K) = 5.067 × 10^21/V J/K. Substituting this value of k in the given expression, we get P = (5.067 × 10^21/V) × V × T = 5.067 × 10^21 T. Therefore, 11eaa948_cd96_c13b_84bc_e5b5942739ad_TB2342_11 is the coefficient of T and 11eaa948_cd96_c13c_84bc_238cd4c63cea_TB2342_11 is zero. The correct choice is B.

The Pressure P of a Gas in a Leak-Tight Container