Answered: Write an expression for the ratio for…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Write an expression for the ratio for ideal combustion of any alkane fuel with chemical formula CxH2x+2. You are essentially looking for a simple function f(x) that satisfies the following relation for any value of x (see attach pic). Show that your function f(x) works for the following alkanes:

a. Methane – CH4

b. Ethane – C2H6

c. Propane – C3H8

Expert Solution

Step 1

To proceed with the problem, we need to know:

Atomic weight of Carbon = 12 g

Atomic weight of Oxygen = 16 g

Atomic weight of Hydrogen = 1 g

The general formula for the combustion of alkanes can be written as:

$C_{n} H_{2 n + 2} + \frac{3 n + 1}{2} O_{2} \to n C O_{2} + (n + 1) H_{2} O$

From the equation written above, it is evident that for any value of n for 1 mole of the alkane, n moles of CO₂ are produced.

Thus f(x) can be written as:

$f (x) = \frac{M a s s o f C O_{2}}{M a s s o f C_{x} H_{2 x + 2}} = \frac{x \times (12 g + 2 \times 16 g)}{x \times 12 g + (2 \times x + 2) \times 1 g}$