Question

56) How much heat energy is required to raise the temperature of 0.298 mole of water from 35.93°C to 79.84" C? The specific heat capacity of water = 4.18 J/g"C A) 13.1 B) 54.7 J C) 985 J D) 2105 J E) 3310J 57) A 43.9-g piece of copper (Ccu= 0.385 J/g*C) at 135.0 C is plunged into 254 g ofwater at 39.0°C. Assuming that no heat is lost to the surroundings, what will the final temperature of the system be? A) 100.0°C B) 40.5°C C) 62.5°C D) 87.0°C E) 53.1°C 58) The molecular weight of urea ((NH2)2CO), a compound used as a nitrogen fertilizer, is amu (rounded to one decimal place). A) 44.0 B) 43.0 C) 60.1 D) 8.0 E) 32.0 59) How many sodium ions are contained in 99.6 mg of Na2SO3? The molar mass of Na2SO3 is 126.05 g/mol. A) 1.52 x 1027 sodium ions B) 4.76 x 1020 sodium ions C) 2.10 x 1021 sodium ions D) 1.05 x 1021 sodium ions E) 9.52 x 1020 sodium ions 60) What is the percent mass of sodium in Na2sO3? SCHRÖDINGER'S CAT IS
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Answer 1

56) INTRODUCTION: The relation to calculate the amount of heat energy required to raise the temperature of a species from an initial temperature to a final temperature is as shown below: q = mC, (T.-T;) ......(1) Here, q is the heat energy, m is the mass of the species, C, is the specific heat capacity of the species, and T, and T, are the final and initial temperatures of the species respectively. SOLUTION: Convert the given moles of water to mass (m) as shown below: Mass = Moles x MolarMass = 0.298 moſ x18g mort = 5.364 g Calculate the heat energy required for water by substituting the given values in equation (i) as shown below: q = mc, (T; -T) = 5.364 g *4.18 JH PA (79.84 – 35.93) % =984.5 J -985 J Hence, the amount of heat energy required to raise the temperature of 0.298 moles of water from 35.93 °C to 79.84 °C is C) 985 J.

57) INTRODUCTION: First you should understand that, since, the temperature of Cu is more than the temperature of water, thus, the heat will flow from the piece of the copper metal to the water until the equilibrium temperature is attained. The heat released by the Copper metal will be equal to the negative of the heat absorbed by the water. The relation to calculate the amount of heat energy absorbed by water is as shown below: qu = m Cpw) (T; -T;) Here, q, is the heat energy absorbed by water, m, is the mass of the water, Cpew) is the specific heat capacity of water, and T, and Tare the final and initial temperatures of the water respectively. The relation to calculate the amount of heat energy lost by copper is as shown below: Icu = mcu@pccu) (T; -T;) ......(ii) Here, qcu is the heat energy lost by copper, mcu is the mass of the copper piece, Cpccu is the specific heat capacity of the copper piece, and T, and T, are the final and initial temperatures of the copper metal respectively. The relation to calculate the final temperature will be as shown below: Heat lost by Cu=-Heat absorbed by water Icu =-9 .....(111) SOLUTION:

Use the given values and substitute equation (i) and (ii) in equation (iii) to calculate the final temperature as shown below: Icu = -9w mc@yucu (T, -T.) = -myCpw (T; -T) 43.98 x0.385Jg* °C*'(T, –135.0)°C =-254 g 4.185 *°C-'(T, –39.0)° C T, = 40.5 °C Hence, the final temperature of the system is B) 40.5 °C 58) INTRODUCTION: The molecular weight of a molecule is calculated by adding the atomic masses of the individual elements. SOLUTION: The number of nitrogen atoms in urea = 2 The number of oxygen atoms in urea = 1 The number of carbon atoms in urea = 1 The number of hydrogen atoms in urea = 4 The atomic mass of nitrogen (A) = 14.0 a.m.u The atomic mass of oxygen (A) = 15.9 a.m.u The atomic mass of carbon (Ac) = 12.0 a.m.u

The atomic mass of hydrogen (A) = 1.0 a.m.u Calculate the molecular weight as shown below: M = 2 Ay +1A, +1Ac +4 A, = 2 x14.0 a.m.u +15.9 a.m.u +12.0 a.m.u + 4x1.0 a.m.u = 59.9 a.m.u = 60.1 a.m.u Hence, the molecular weight of urea is C) 60.1 a.m.u. 59) INTRODUCTION: 1 mol of a substance contains 6.022 x 10 number of species. The relation to calculate the moles of a species is as shown below: Mass Moles = Molar mass ...... (1) SOLUTION: Calculate the moles of Na,SO, using equation (i) as shown below: Mass Moles = Molar mass 99.6x10- 8 126.05 g mol! = 7.9x10-6 mol

1 atom of Na,so, contains = 2 ions of Na 1 mol of Na,so, contains = 2 moles of ions of Na 7.9 x10-4 mol of Na,so, contains = 2x7.9x10-4 =1.58x10*molof ions of Na Calculate the number of ions of Na as shown below: Number of Na ions = 1.58x10- mof x 6.022x10-23 ion mort = 9.52x100 ions Hence, the number of ions of Na is E) 9.52x1020 ions 60) INTRODUCTION: The relation to calculate the mass percent is as shown below: Molar mass of the element whose mass % is to be calculated Mass %=M - Molar mass of the compound 100% SOLUTION: Calculate the mass % using the above relation as shown below: Molar mass of Na Mass % of Na= -X100% Molar mass of the Na SO, 22.98 amu *100% 126.05 amu = 0.1823x100% =18.23% Hence, the mass percent of sodium in Na S03 is 18.23%