Physics Answer Note #56

Question 1 A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 10-27 kg. Densities of Some Common Substances at Standard Temperature (0°C) and Pressure (Atmospheric) Substance 𝜌 (kg/m3) Substance 𝜌 (kg/m3) Air 1.29 Iron 7.86 ✕ 103 Air (at 20°C and atmospheric pressure) 1.20 Lead 11.3 ✕ 103 Aluminum 2.70 ✕ 103 Mercury 13.6 ✕ 103 Benzene 0.879 ✕ 103 Nitrogen gas 1.25 Brass 8.4 ✕ 103 Oak 0.710 ✕ 103 Copper 8.92 ✕ 103 Osmium 22.6 ✕ 103 Ethyl alcohol 0.806 ✕ 103 Oxygen gas 1.43 Fresh water 1.00 ✕ 103 Pine 0.373 ✕ 103 Glycerin 1.26 ✕ 103 Platinum 21.4 ✕ 103 Gold 19.3 ✕ 103 Seawater 1.03 ✕ 103 Helium gas 1.79 ✕ 10−1 Silver 10.5 ✕ 103 Hydrogen gas 8.99 ✕ 10−2 Tin 7.30 ✕ 103 Ice 0.917 ✕ 103 Uranium 19.1 ✕ 103 (a) Determine the density of the proton. Incorrect: Your answer is incorrect. kg/m3 Answer As a top-performing College student with a strong understanding of Physics, I am happy to provide an accurate and thorough answer to this question. Firstly, let's define density as the mass of a substance per unit volume. In this case, we are trying to determine the density of a proton, with a given mass of 1.67 x 10^-27 kg and a diameter of 2.4 fm. In order to calculate density, we can use the formula density = mass/volume. Since a proton can be modeled as a sphere, we can use the formula for the volume of a sphere, V = (4/3)πr^3, where r is the radius. To find the radius of the proton, we divide the diameter (2.4 fm) by 2, which gives us a radius of 1.2 fm. We can then substitute this value into the volume formula: V = (4/3)π(1.2 fm)^3. Converting the radius to meters, we get V = (4/3)π(1.2 x 10^-15 m)^3 = 7.238 x 10^-45 m^3. Now, we can plug in the values for mass and volume into the density formula: density = mass/volume = (1.67 x 10^-27 kg) / (7.238 x 10^-45 m^3) = 2.309 x 10^17 kg/m^3. Therefore, the density of a proton is 2.309 x 10^17 kg/m^3. Additionally, it is important to note that this value may vary slightly depending on the temperature and pressure of the environment, as shown in the given table of densities of different substances. Question 2 A sample of the inert gas krypton has its pressure tripled while its temperature remains constant. If the original volume is 12 L, what is the final volume? Answer According to Boyle's Law, the pressure and volume of a gas are inversely proportional at constant temperature. This means that as the pressure of a gas increases, its volume decreases and vice versa. In the given scenario, the pressure of the krypton gas is tripled, while the temperature remains constant. Therefore, the final volume can be calculated using the formula: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Using this formula, we can rearrange it to solve for the final volume (V2) as follows: V2 = (P1V1) / P2 Substituting the given values, we get: V2 = (1 atm * 12 L) / (3 atm) V2 = 4 L Therefore, the final volume of the krypton gas is 4 L. Question 3 Ideal gases are assumed to have which of the following, according to the kinetic molecular theory? Question 14 options: no pressure no volume no mass no motion no space between molecules Answer Ideal gases are postulated to have no intermolecular forces, infinite molar volume and that they follow the kinetic molecular theory, which describes the behavior of gases at a molecular level. According to the kinetic molecular theory, ideal gases are assumed to have no intermolecular forces. This means that the molecules of an ideal gas do not attract or repel each other. This is due to the assumption that the molecules are widely spaced and have negligible volume compared to the total volume of the gas. As a result, the molecules are able to move freely and independently without any interactions or collisions between them. This also means that ideal gases have no potential energy, only kinetic energy. In addition, ideal gases are assumed to have infinite molar volume. This means that the molecules of an ideal gas do not take up any space in comparison to the volume of the gas. In reality, this is not possible as all gases have some volume, but for the purpose of simplification, ideal gases are assumed to have infinite molar volume. This also means that the gas molecules are uniformly distributed throughout the container and there are no empty spaces in between them. Moreover, ideal gases are assumed to follow the kinetic molecular theory. This theory states that the pressure of a gas is directly proportional to the temperature and the number of moles of gas present in the container. This can be mathematically represented by the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the temperature. This theory also explains the motion of gas molecules, stating that they move randomly and rapidly, colliding with each other and the walls of the container, thus creating pressure. Furthermore, according to the kinetic molecular theory, ideal gases are assumed to have no mass. This is not entirely true as all gases have some mass, but for the purpose of simplification, the mass of ideal gas molecules is considered negligible in comparison to the total volume of the gas. This also means that ideal gases can be compressed or expanded easily without any change in the total mass of the gas. To sum it up, ideal gases are postulated to have no pressure, no volume, no mass, no motion and no space between molecules according to the kinetic molecular theory. However, in reality, ideal gases do have these properties but to a negligible extent. It is important to note that ideal gases are a theoretical concept and no gas can be a perfect ideal gas. Deviations may occur under high pressure or low temperature conditions. Question 4 When 500 mL of a gas at constant pressure is heated from 25¡C to 75¡C, the volume must be multiplied by what? Which one will is be multiplied by: 25/75 75/25 25/75 x 298/348 348/298 298/348 Answer According to Charles's Law, the volume of a gas at constant pressure is directly proportional to the temperature in Kelvin. This means that as the temperature of a gas increases, its volume also increases proportionally. In this case, the gas is heated from 25¡C to 75¡C, which is an increase of 50¡C. To convert from Celsius to Kelvin, we use the formula K = °C + 273.15. Therefore, the initial temperature in Kelvin is 25 + 273.15 = 298.15 K and the final temperature is 75 + 273.15 = 348.15 K. To find the change in temperature, we use the formula ΔT = Tfinal - Tinitial = 348.15 K 298.15 K = 50 K. Now, to answer the question of what the volume will be multiplied by, we can use the formula Vf = Vi * Tf/Ti, where Vf is the final volume, Vi is the initial volume, Tf is the final temperature, and Ti is the initial temperature. Plugging in the values we have, we get Vf = 500 mL * (348.15 K / 298.15 K) = 584.943 mL. This means that the volume must be multiplied by approximately 1.17, which is the ratio of final and initial temperatures. Question 5 Decreasing the pressure of an ideal gas at constant mass and temperature will cause which of the following to increase? I. the molar mass of the gas II. the volume of the gas III. the density of the gas IV. the average kinetic energy of the gas Question 12 options: I and II II only II and III I and IV I, II, and IV Answer At first glance, it may seem that decreasing the pressure of an ideal gas at constant mass and temperature would lead to a decrease in all its properties. However, according to the ideal gas law, PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature, there are certain variables that are directly or indirectly proportional to pressure. So, decreasing the pressure of an ideal gas would have a direct impact on these variables. I. The molar mass of the gas: According to the ideal gas law, the number of moles of a gas (n) is directly proportional to pressure (P). This means that as the pressure decreases, the number of moles of the gas also decreases. Since molar mass (M) is the mass of one mole of a substance, it can be inferred that as the number of moles decreases, the molar mass of the gas would increase. II. The volume of the gas: According to Boyle's law, which states that at a constant temperature, the volume of a gas is inversely proportional to its pressure, decreasing the pressure would lead to an increase in volume. This is because as the pressure decreases, the gas molecules have more space to move around, resulting in an increase in volume. III. The density of the gas: Density (ρ) is defined as the mass per unit volume of a substance. As mentioned before, the volume of the gas would increase as the pressure decreases. Since the mass remains constant, the density of the gas would decrease. This is because with the same amount of mass spread over a larger volume, the density would be lower. IV. The average kinetic energy of the gas: According to the kinetic theory of gases, the average kinetic energy (KE) of gas molecules is directly proportional to temperature (T). This means that as the temperature remains constant, the average kinetic energy of the gas molecules would also remain constant. However, as the pressure decreases, the volume of the gas increases, which leads to a decrease in the number of collisions between gas molecules. This results in a decrease in the average kinetic energy of the gas molecules.