Responses: a. 1.28 mol/L; b. 17.0 %; c. 0.0227; d. 1.29 mol/kg Explanation: a. Molar concentration: c = moles/litres. Moles = 167 × 1/159.61. After performing the calculation, Moles = 1.046 mol. Litres = 820 × 1/1000. Hence, Litres = 0.8200 L. Calculating the molar concentration gives c = 1.046/0.8200, resulting in c = 1.28 mol·L⁻¹. b. Percent by mass: Mass % = mass of solute / mass of solution × 100 %. Mass of solution = volume × density, therefore, Mass of solution = 820 × 1.195. By calculating this, Mass of solution = 979.9 g. Thus, Mass % = 167/979.9 × 100, which results in Mass % = 17.0 %. c. Mole fraction: χ = moles of solute / (moles of solvent + moles of solute). Mass of solvent = mass of solution – mass of solute; namely, Mass of solvent = 979.9 – 167. Converting this to moles gives Moles of water = 812.9 × 1/18.02, which results in Moles of water = 45.11 mol. The total moles are 1.046 + 45.11, leading to Total moles = 46.16 mol. Finally, the mole fraction is calculated as χ = 1.046/46.16, equating to χ = 0.0227. d. Molal concentration: b = moles of solute / kilograms of solvent. Mass of solvent = 812.9 g = 0.8129 kg. Therefore, the molal concentration yields: b = 1.046/0.8129 = 1.29 mol/kg.
Response:1816.6 joules
Clarification:refer to the attached image
The new pressure of the gas is calculated to be 40.7 kPa. Using the principle that P1 • V1 = P2 • V2, we can set 98.8 kPa (P1) multiplied by 21.7 mL (V1) equal to P2 (unknown pressure) multiplied by 52.7 mL (V2). To isolate P2, we rearrange the equation to P2 = (98.8 kPa • 21.7 mL) / 52.7 mL, resulting in P2 equal to 40.7 kPa.
Response: k = 23045 N/m
Clarification:
To determine the spring constant, one must consider the maximum elastic potential energy that the spring can withstand. The kinetic energy of the vehicle should equal at minimum the elastic potential energy of the spring when it is fully compressed. Hence, we express it as:
(1)
M: mass of the vehicle = 1050 kg
k: spring constant =?
v: car speed = 8 km/h
x: maximum spring compression = 1.5 cm = 0.015m
You need to resolve equation (1) for k. Beforehand, convert the speed v to meters per second:
The spring constant calculates to 23045 N/m
