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tresset_1 [31]
3 years ago
5

What is the molar concentration of [H3O+] in a cola that has a pH of 3.120?

Chemistry
1 answer:
ELEN [110]3 years ago
8 0

Answer:

  • [H₃O⁺] = 7.586×10⁻⁴ M

Explanation:

The <em>pH</em> of a solution is a measure of the <em>molar concentration of </em><em>H₃O⁺</em> ions in the solution.

The mathematical expresssion that states the relation between the molar concentration of H₃O⁺ ions and the pH of the solution is:

  • pH = - log [H₃O⁺].

This is pH is numerically equal to the negative decimal logarithm of the  molar concentration of H₃O⁺.

The square brackets are used to indicate molar concentration.

Thus:

  • pH = - log [H₃O⁺] ← equation
  • 3.120 = -log [H₃O⁺] ← substituting values
  • - 3.120 = log [H₃O⁺] ← product property of the multiplication
  • 10^{- 3.120}=[H_3O^+] ← antilogarithm property
  • [H₃O⁺] = 7.586×10⁻⁴ M ← result
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A 232-lb fullback runs the 40-yd dash at a speed of 19.8 ± 0.1 mi/h.
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(b)  1.11 x 10⁻³⁵ m

Explanation:

(a)  The de Broglie wavelength is given by the expression:

λ = h/p = h/mv

where h is plancks constant, p is momentum which is equal to mass times velocity.

We have all the data required to calculate the wavelength, but first we will have to convert the velocity to m/s, and the mass to kilograms to work in metric system.

v = 19.8 mi/h x ( 1609.34 m/s ) x ( 1 h / 3600 s ) = 8.85 m/s

m = 232 lb x ( 0.454 kg/ lb ) = 105.33 kg

λ = h/ mv = 6.626 x 10⁻³⁴ J·s / ( 105.33 kg x 8.85 m/s ) = 7.11 x 10⁻³⁷ m

(b) For this part we have to use the uncertainty principle associated with wave-matter:

ΔpΔx > = h/4π

mΔvΔx > = h/4π

Δx = h/ (4π m Δv )

Again to utilize this equation we will have to convert the uncertainty in velocity to m/s for unit consistency.

Δv = 0.1 mi/h x ( 1609.34 m/mi ) x ( 1 h/ 3600 s )  

     = 0.045 m/s

Δx = h/ (4π m Δv ) = 6.626 x 10⁻³⁴ J·s / (4π x 105.33 kg x 0.045 m/s )

     = 1.11 x 10⁻³⁵ m

This calculation shows us why we should not be talking of wavelengths associatiated with everyday macroscopic objects for we are obtaining an uncertainty of 1.11 x 10⁻³⁵ m for the position of the fullback.

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3 years ago
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