Question

The first two problems are to be submitted today. 1.(25PTS) At midday on the lunar surface, a temperature of 98 95°C was recorded Calculate the average speed of Neg) in m/s and mile/hr under these conditions. The formula for the average speed can be derived from the kinetic theory of gases and it is given by SRT average_speed= (molar mass) 2. (25PTS) Data: R -0,0821 L atm/K mole) -8.314 JAK mole). Atomic mass Ne-20.18 A reaction that can be used to inflate air bags is 2 NaN,(s) -----> 2 Na(s) + 3 N.(g) In a lab simulation, 18.7 mL of N_(g) were obtained at a pressure of 745 torr and 22.8°C. Assuming there were no side reactions, how many grams of NaN,(s) reacted? Data: Atomic masses: N-14.01, Na -22.99 The next two problems are due next week, but work on these problems today with your group. 3.(25PTS) At a water treatment facility, an 750.0L tank containing Cl:(8) has a pressure of 62.0 atm and a temperature of 303 K © Using ideal gas equation, determine the moles of Cl_(8) present. (1) What pressure would be expected if this same amount of gas occupied the same volume at the same temperature, but the Cl obeyed the Van der Waals equation of state? a-6.49 atm L/mol, and b=0.0562 L/mol Data: Atomic mass Cl = 35.45 4.(25PTS) Explosives are effective if they produce a large number of gaseous molecules as products, Nitroglycerin, for example, detonates as follows: 2 CH NOXI) ---> 6 CO (8) +3 N() +5H.0() + ) I 1.90 g of nitroglycerin explodes, calculate the volume in liters) that the product gases would occupy if their total pressure is 1.60 atm at 4.95 x10 °C. Data: Atomic masses H=1.008, N-14.01, 0-16.00, C12.01 Hints: Compute the total number of moles of gases then use the ideal gas equation Optional Bonus Problem (+4pts) No partial credit. Suppose you are given exactly 1 Liter of a 2.75 x 10' M solution of toluene C.HSCH, dissolved in benzene C.H... Exactly 1 milliliter of this solution is taken and diluted to exactly 1 liter with benzene. Call the resulting solution #2. Next take exactly 1 ml of solution #2 and dilute it to exactly 1 liter with benzene. Call the resulting solution #3. Continue in this manner until you get to solution 18. What is the concentration of solution #8? Calculate the number of molecules of toluene in 1 liter of solution #8. Interpret your result.

Answer 1

1.

Average speed (Ca) = $\sqrt{\frac{8RT}{\pi M}}$

For Ne gas molar mass (M) = 20.18 g /mol

= 20.18 ×10^-3 Kg/mol.

T =98.95 +273 = 371.95 K

average speed for Ne at this temperature

Ca = $\sqrt{\frac{8 \times 8.314 \times 371.95}{3.14 \times 20.18 \times 10^{-3}}}$

or, Ca = 624.83 m/s.

now , average speed in mile /hr

= 624.83  $\frac{m}{s}$ × $\frac{1 \: Km }{1000 \: m}$ × $\frac{0.62137 \: mile }{1\: Km}$ × $\frac{60 \: s }{1\: min}$ ×$\frac{60 \: min}{1\: hr}$

= 1397.7 mile/hr.

2.

Ideal gas equation is

PV = nRT

or, n = PV/RT

P = 745 torr = (745/760) = 0.98 atm

T = 22.8+273= 295.8 K.

R = 0.082 L -atm/mol.K

V = 18.7 mL = 0.0187 L

number of moles (n)

= (0.98×0.0187/0.082×295.8)

= 0.00075

from balanced reaction 3 mole N₂ is produced by 2 mole NaN₃ .

hence, moles of NaN₃ reacted = 0.00075 × $\frac{2}{3}$ = 0.00050

molar mass of NaN₃ = 22.99 + ( 14.01×3) = 65.02 g/mol.

mass of NaN₃ reacted

= moles × molar mass

= 0.00050 × 65.02

= 0.03251 g.