For the first-order decomposition, the equation is: ln(x0 / x) = kt. At t = 200, x = 0.0300 M, we have ln(x0 / 0.03) = 200k. At t = 400, when x = 0.0200 M, we utilize ln(x0 / 0.02) = 400k. By multiplying the first equation by 2, we get 2ln(x0 / 0.03) = 400k, which aligns with the second equation, leading us to conclude that 2ln(x0 / 0.03) = ln(x0 / 0.02). This suggests (x0 / 0.03)^2 = x0 / 0.02, allowing us to find x0 = 0.045 M as the initial concentration. Plugging this back into the first equation yields: ln(0.045 / 0.03) = 200k, from which it follows that k = 0.0020273 (rate constant). The half-life can be calculated with x = 0.5x0: ln(x0 / 0.5x0) = 0.0020273t, resulting in ln(2) = 0.0020273t, which simplifies to t = 341.90 minutes (half-life).
From the provided data, the unknown mixture was composed of salt, salicylic acid, and sand. It is understandable that the student suspected the presence of sand, yet scientific experimentation must verify such assumptions. The test involving salt and salicylic acid reveals that salt dissolves in water, while salicylic acid is only slightly soluble, and sand does not dissolve at all. By introducing the unknown into water, the salt would dissolve first, followed by the partial dissolution of salicylic acid. Heating the mixture could allow for the evaporation of salicylic acid, resulting in the remaining salt. If traces of sand were observed in the dissolved sample, it could suggest contamination.
Answer:
a) 
b) 1657 €
Explanation:
Hola,
a) En esta cuestión analizaremos el millón de litros de agua anualmente, dado que este dato nos permite calcular el calor necesario para calentar dicha cantidad, considerando que la densidad del agua es de 1 kg/L:
A continuación, utilizamos la entalpía de combustión del metano para determinar la cantidad en kilogramos necesaria, ya que la energía calórica perdida por el metano es equivalente a la energía obtenida por el agua:
b) En este supuesto, tenemos que, bajo condiciones normales de 1 bar y 273 K, el precio de 1 metro cúbico de metano es 0,45 €, lo que nos permite calcular las moles de metano en esas condiciones:
En consecuencia, los kilogramos de metano que se obtienen por 0,45 € son:
Finalmente, usando regla de tres:
0.715 kg ⇒ 0.45 €
2630 kg ⇒ X
X = (2630 kg x 0.45 €) / 0.715 kg
X = 1657 €
Regards.
