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2009_Midterm_1_Key

2009_Midterm_1_Key - Mid Term 1 Solutions Question 1a Zn(s...

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Mid Term 1 - Solutions Question 1a Zn ( s ) + 2HCl ( aq ) ZnCl 2( s ) + H 2( g ) Mg ( s ) + 2HCl ( aq ) MgCl 2( s ) + H 2( g ) or Zn ( s ) + 2H 3 O + ( aq ) Zn 2+ ( s ) + H 2( g ) + 2H 2 O ( aq ) Mg ( s ) + 2H 3 O + ( aq ) Mg 2+ ( s ) + H 2( g ) + 2H 2 O ( aq ) Question 1b m(Zn) + m(Mg) = 1 . 87g (1) n(H 2 ) = n(Zn) + n(Mg) (2) n( H 2 ) = m( H 2 ) M(H 2 ) = 0 . 151g 2 . 016g mol - 1 = 0 . 0749mol (3) n(HCl) = 3mol in excess! (4) 0 . 0749 = m(Zn) 65 . 409gmol - 1 + m(Mg) 24 . 305gmol - 1 (5) 0 . 0749 = m(Zn) 65 . 409gmol - 1 + 1 . 87g - m (Zn) 24 . 305gmol - 1 (6) m(Zn) = 0 . 0788g (7) w%(Zn) = 4 . 22% (8) Important: 3 significant figures. Question 2a W = 3 . 4 × 10 - 19 J h ν = KE + W (9) 1
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hc λ = KE + W (10) To find the longest wavelength (i.e. smallest energy) KE = 0 (11) λ = hc W = 6 . 626 × 10 - 34 Js × 2 . 997 × 10 8 ms - 1 3 . 4 × 10 - 19 J = 5 . 84 × 10 - 7 m = 584nm (12) Question 2b p = h λ (13) p = mv (14) Estimates: Tennis ball mass = 50g, Serve speed = 150 mph 150mph 240km h - 1 66 . 7ms - 1 mv = h λ (15) λ = h mv = 6 . 626 × 10 - 34 Js 50 × 10 - 3 kg × 66 . 7ms - 1 = 2 × 10 - 34 m (16) Question 3a Δx = 1 . 5 ˚ A = 1 . 5 × 10 - 10 m (17) Δ p Δ x h 4 π (18) Δp 5 . 27 × 10 - 35 Js 1 . 5 × 10 - 10 m (19) Δp 3 . 5 × 10 - 25 kgms - 1 (20) Question 3b n 1 = 1; n 2 = 2 E n = n 2 h 2 8mL 2 (21) 2
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Δ E n i ,n f = (n 2 f - n 2 i ) h 2 8m e L 2 (22) Δ E
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