Question

2) Methane, CH_{4}, is the principal ingredient of
natural gas. The chemical equation for the chemical burning of
methane is 2O_{2}+CH_{4} --------2H_{2}O + CO_{2} . 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.

Answer #1

(2). (a). Given: 2O_{2}
+ CH_{4}
2H_{2}O + CO_{2}

Moles of CH_{4} 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.

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