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A chemistry student needs to determine the conditions required for a liquid mixture of water and ethanol to boil at a temperature of exactly 80°C. What is the minimum percentage of ethanol needed in the mixture and at what pressure should it be boiled in order to achieve this specific boiling point?

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To determine the minimum percentage of ethanol needed in the mixture and the pressure at which it should be boiled to achieve a boiling point of 80C, we can use the concept of Raoult's Law. Raoult's Law states that the partial vapor pressure of each component in a solution is equal to the product of the mole fraction of the component and its vapor pressure as a pure substance.Let x1 be the mole fraction of water and x2 be the mole fraction of ethanol in the mixture. Since there are only two components, x1 + x2 = 1.The vapor pressure of pure water  P1  at 80C can be found using the Antoine equation, which is given by:log10 P1  = A - B /  C + T For water, A = 8.07131, B = 1730.63, and C = 233.426. The temperature, T, should be in Celsius.log10 P1  = 8.07131 - 1730.63 /  233.426 + 80 P1 = 10^2.337  = 217.42 mmHgSimilarly, the vapor pressure of pure ethanol  P2  at 80C can be found using the Antoine equation with the constants for ethanol: A = 8.20417, B = 1642.89, and C = 230.3.log10 P2  = 8.20417 - 1642.89 /  230.3 + 80 P2 = 10^2.883  = 760.96 mmHgNow, we can apply Raoult's Law to find the mole fractions of water and ethanol:P_total = x1 * P1 + x2 * P2Since we want the mixture to boil at 80C, the total pressure  P_total  should be equal to the atmospheric pressure at the boiling point, which is approximately 760 mmHg.760 = x1 * 217.42 +  1 - x1  * 760.96Solving for x1, we get:x1 = 0.914Now, we can find the mole fraction of ethanol  x2 :x2 = 1 - x1 = 1 - 0.914 = 0.086To find the percentage of ethanol by volume, we can use the density of each component to calculate the volume fraction. The density of water at 80C is approximately 0.9718 g/mL, and the density of ethanol at 80C is approximately 0.7893 g/mL.Let V1 and V2 be the volume fractions of water and ethanol, respectively. We can write the following equation:x1 =  V1 * 0.9718  /  V1 * 0.9718 + V2 * 0.7893 Substituting x1 = 0.914, we get:0.914 =  V1 * 0.9718  /  V1 * 0.9718 + V2 * 0.7893 Solving for V1 and V2, we get:V1 = 0.9718 * V2 /  0.7893 *  1 - 0.914  V1 = 4.64 * V2Now, the volume percentage of ethanol can be calculated as:% ethanol =  V2 /  V1 + V2   * 100% ethanol =  1 /  4.64 + 1   * 100 = 17.76%Therefore, the minimum percentage of ethanol needed in the mixture is approximately 17.76% by volume. The mixture should be boiled at atmospheric pressure  approximately 760 mmHg  to achieve a boiling point of 80C.

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