Аеростат об’ємом 250 м3 необхідно заповнити воднем за температури 27 °С і нормального атмосферного тиску. Скільки електроенергії потрібно витратити, пропускаючи струм через слабкий розчин сірчаної кислоти, для того щоб отримати необхідну кількість водню, якщо ККД установки для електролізу дорівнює 80 %? Електроліз ведеться за напруги 20 В.
You will need to apply the equation for calculating the amount of energy required for electrolysis: E = V x I x t. Since we know the voltage (20 V) and efficiency (80%), we can calculate the amount of current needed. First, convert the volume of the balloon from cubic meters to cubic centimeters by multiplying by 1000000. This gives us 250000000 cm3 of hydrogen. Using the molar mass of hydrogen (1.008 g/mol) and Avogadro's number (6.022x10^23), we can calculate the number of moles of hydrogen needed: 250000000 x 1.008 / 6.022x10^23. This gives us approximately 4.18x10^-17 moles of hydrogen. Since electrolysis generates one mole of hydrogen for every two moles of electrons, we need half of this amount in terms of electrons: 2.09x10^-17 electrons. Now, we can use the equation Q = I x t to calculate the charge needed for electrolysis. Substituting in the current (I) from before, we get Q = 2.09x10^-17 x t. Since we know the voltage (20 V), we can solve for t: t = Q / V x I. Plugging in the amount of charge needed and the voltage, we get a time of approximately 4.18x10^-16 seconds. Now, we can use the equation for calculating energy to get the final answer. Energy (E) = V x I x t. Substituting in the values, we get E = 20 x 4.18x10^-17 x 4.18x10^-16, which gives us a final answer of approximately 3.5x10^-16 J, or 3.5x10^-16 V x A x s. Keep in mind, this is the minimum amount of energy needed and it is based on ideal conditions. In reality, there are always some inefficiencies in the process, so you may need to use slightly more energy. Additionally, please be mindful of safety precautions when working with hydrogen gas. Good luck with your project!
