When 1 gram of ethane is burned, 52 kJ of heat is released, and 1 gram of butane – 49.7 kJ of heat. During the combustion of a mixture of these alkanes weighing 35.6 g, 1822 kJ of heat was released. Find the mass fraction of substances in the initial mixture
Denote the mass of ethane by “x”, and the mass of butane – by “y”. Based on this, we compose an equation showing the dependence of the components by mass, we obtain:
x + y = 36.5
The energy dependence is displayed by the equation:
52x + 49.7y = 1822 or 52x + 49.7 (35.6 – x) = 1822
We calculate the mass of ethane in the mixture from the last equation, we get:
52x + 49.7 (35.6 – x) = 1822;
52x + 1769.32 – 49.7x = 1622;
2.3x + 1769.32 = 1822;
2.3x = 52, 69;
x = 22.9 g.
Find the mass fraction of substances in the initial mixture:
w% (ethane) = (100.22.9) / 35.6 = 64.33%;
w% (butane) = 100% – 64.33% = 35.67%.
Answer: w% (ethane) = 64.33%; w% (butane) = 35.67%
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