When 1 gram of ethane is burned, 52 kJ of heat is released, and 1 gram of butane – 49.7 kJ of heat

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

Decision:
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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