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ioda
3 years ago
11

How long must $542 be invested at a rate of 7% to earn $303.52 in interest

Chemistry
1 answer:
yulyashka [42]3 years ago
7 0

The number of years that must be invested at  a rate of 7 % to earn$ 303.52 in interest is

    8 years

 <em><u>calculation</u></em>

  • <em><u> </u></em><em>by use of  the formula       A = P (1+  rt) </em>
  • <em>  where :  A  is the final amount  =  542 + 303.52  =$ 845.52</em>

<em>                    P  is the principal   money to be invested =  $ 542</em>

<em>                        r= rate= 7/100=0.07</em>

<em>                       t=  time required</em>

<em>=$ 845.52=$ 542( 1+  0.07 t)</em>

  • <em>open the  bracket</em>
  • <em>= $845.53= $542 + $37.94  t</em>

  • <em>like terms  together</em>

    =$  845.53 -$542  = $37.94 t

   =$303.52 =$37.94 t

  • divide both  side by  $37.94

  =  $303.52/ $   37.94  =  $37.94t/$37.94

  t=  8 years

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Answer:

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Explanation:

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7. A 2.0 L container had 0.40 mol of He(g) and 0.60 mol of Ar(g) at 25°C.
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a) Ek Ar > Ek He

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c) If v Ar = 431 m/s ⇒ v He = 1710.44 m/s

d) Pt = 12.218 atm

e) P He = 4.887 atm and P Ar = 7.33 atm

Explanation:

container:

∴ V = 2.0 L

∴ n He = 0.4 mol

∴ n Ar = 0.6 mol

∴ T = 25°C ≅ 298 K

a) Internal energy (U) :

∴ U = Ek + Ep = kinetic energy + potential energy

∴ Ep: the potential interaction energy is neglected, assuming ideal gas mixture

⇒ U = Ek = N(1/2mv²)= 3/2 NKT

∴ N = nNo ....number of moleculas

∴ K = 1.380 E-23 J/K....Boltzmann's constant

∴ No = 6.022 E23 molec/mol....Avogadro's number

for He:

⇒ N = (0.4)(6.022 E23) = 2.4088 E23 molec

⇒ Ek = (3/2)(2.4088 E23)(1.380 E-23 J/K)(298) = 1485.892 J

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⇒ N = (0.6)(6.022 E23) = 3.6132 E 23 molec

⇒ Ek = (3/2)(3.6132 E23)(1.380 E-23 J/K)(298) = 2228.838 J

** Ar gas has a greater average kinetic energy

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∴ N(1/2)mv² = (3/2)NKT

⇒ mv² = 3KT

⇒ v² = 3KT/m

⇒ v = √3KT/m

∴ m He = (0.4 mol)(4.0026 g/mol) = 1.601 g He = 1.601 E-3 Kg He

⇒ v = √(3(1.380 E-23)(298)/(1.601 E-3)) = 2.776 E-9 m/s He

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e) P He = nRT/V = (0.4)(0.082)(298)/2 = 4.8872 atm

⇒ P Ar = Pt - PHe = 12.218 - 4.8872 = 7.33 atm

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