Question

# 2) Methane, CH4, is the principal ingredient of natural gas. The chemical equation for the chemical...

2) Methane, CH4, is the principal ingredient of natural gas. The chemical equation for the chemical burning of methane is 2O2+CH4 --------2H2O + CO2 . It is midwinter in New Jersey. To keep the house warm, the owner is burning 120 moles of methane per hour. Compute the rate (in moles per hour) at which oxygen is being consumed in the process. Let x denote the amount of methane (in moles) consumed durign the burning. Let y denote the amount of oxygen consumed during the burning.

a)Given:

b) Want to Find:

c) Find equation relating x and y: Be careful! The chemical equation, (1), is NOT the required linking, though it is related to that condition. (Hint: Create a table of x-values and corresponding y values. Then find the related equation, y in terms of x.)

d) Differentiate to find the unknown rate of change.

(2). (a). Given: 2O2    +     CH4         2H2O +     CO2

Moles of CH4 burned per hour = 120

(b). To find: Rate at which O2 is consumed and relation between x and y.

(c). Amount of methane consumed = x

Amount of O2 consumed = y

From the equation we can see that, 2 moles of O2 are consumed per mole of CH4.

So,

y = 2x

(d). Differentiating y = 2x w.r.t time:

dy / dt = 2 dx / dt

dy / dt = 2 * 120

dy / dt = 240

Hence, rate of O2 consumed = 240 moles / hr.