Consider a hypothetical reaction between a, b, and c that is first order in a, zero order in b, and second order in c. (a) write the rate law for the reaction. (b) how does the rate change when [a] is doubled and the other reactant concentrations are held constant? (c) how does the rate change when [b] is tripled and the other reactant concentrations are held constant? (d) how does the rate change when [c] is tripled and the other reactant concentrations are held constant? (e) by what factor does the rate change when the concentrations of all three reactants are tripled? (f) by what factor does the rate change when the concentrations of all three reactants are cut in half?

(a) Rate = k[A][B]⁰[C]² = k[A][C]².

(b) The rate of the reaction will be doubled as the the rate of the reaction will be doubled.

(c) The rate of the reaction will not be changed as the rate of the reaction is zero order for B and does not depend on the concentration of reactant B.

(d) The rate of the reaction will increase by a factor of 9 when [C] is tripled and the other reactant concentrations are held constant.

(e) The rate of the reaction will increase by a factor of 27 the concentrations of all three reactants are tripled.

(f) The rate of the reaction will decrease by a factor of 8  the concentrations of all three reactants are cut in half.

Explanation:

(a) Write the rate law for the reaction.

The rate of the reaction is the change in the concentration of the reactants (decrease) or the products (increase) with time.

Rate = ΔConcentration/Δt.

The rate of the reaction is directly proportional to the concentration of the reactants.

R ∝ [A][B][C].

Since the mentioned reaction is first order in A, zero order in B, and second order in C.

∴ Rate = k[A][B]⁰[C]² = k[A][C]²,

where, k is the rate constant of the reaction.

(b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant?

If we consider the concentration of [A₁] = [A₀].

As the concentration of [A] is doubled, [A₂] = [2A₀]. [B] and [C] are held constant.

∴ Rate₁ = k[A₁][B₁]⁰[C₁]² = k[A₀][B₀]⁰[C₀]²

Rate₂ = k[A₂][B₂]⁰[C₂]² = k[2A₀][B₀]⁰[C₀]²

∴ Rate₁/Rate₂ = (k[A₀][B₀]⁰[C₀]²)/(k[2A₀][B₀]⁰[C₀]²) = 1/2.

∴ Rate₂ = 2(Rate₁).

So, the rate of the reaction will be doubled.

(c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant?

If we consider the concentration of [B₁] = [B₀].

As the concentration of [A] is doubled, [B₂] = [3B₀]. [A] and [C] are held constant.

∴ Rate₁ = k[A₁][B₁]⁰[C₁]² = k[A₀][B₀]⁰[C₀]²

Rate₂ = k[A₂][B₂]⁰[C₂]² = k[A₀][3B₀]⁰[C₀]²

∴ Rate₁/Rate₂ = (k[A₀][B₀]⁰[C₀]²)/(k[A₀][3B₀]⁰[C₀]²) = 1.

∴ Rate₂ = (Rate₁).

So, the rate of the reaction will not be changed as the rate of the reaction is zero order for B and does not depend on the concentration of reactant B.

(d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant?

If we consider the concentration of [C₁] = [C₀].

As the concentration of [A] is doubled, [C₂] = [3C₀]. [A] and [B] are held constant.

∴ Rate₁ = k[A₁][B₁]⁰[C₁]² = k[A₀][B₀]⁰[C₀]²

Rate₂ = k[A₂][B₂]⁰[C₂]² = k[A₀][B₀]⁰[3C₀]²

∴ Rate₁/Rate₂ = (k[A₀][B₀]⁰[C₀]²)/(k[A₀][B₀]⁰[3C₀]²) = 1/9.

∴ Rate₂ = 9(Rate₁).

So, the rate of the reaction will increase by a factor of 9.

(e) By what factor does the rate change when the concentrations of all three reactants are tripled?

If we consider the concentration of [A₁] = [A₀], [B₁] = [B₀], and [C₁] = [C₀].

As the concentration of all three reactants are tripled:

[A₂] = [3A₀], [B₂] = [3B₀], and [C₂] = [3C₀].

∴ Rate₁ = k[A₁][B₁]⁰[C₁]² = k[A₀][B₀]⁰[C₀]²

Rate₂ = k[A₂][B₂]⁰[C₂]² = k[3A₀][3B₀]⁰[3C₀]²

∴ Rate₁/Rate₂ = (k[A₀][B₀]⁰[C₀]²)/(k[3A₀][3B₀]⁰[3C₀]²) = 1/27.

∴ Rate₂ = 27(Rate₁).

So, the rate of the reaction will increase by a factor of 27.

(f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

If we consider the concentration of [A₁] = [A₀], [B₁] = [B₀], and [C₁] = [C₀].

As the concentration of all three reactants are tripled:

[A₂] = [1/2A₀], [B₂] = [1/2B₀], and [C₂] = [1/2C₀].

∴ Rate₁ = k[A₁][B₁]⁰[C₁]² = k[A₀][B₀]⁰[C₀]²

Rate₂ = k[A₂][B₂]⁰[C₂]² = k[1/2A₀][1/2B₀]⁰[1/2C₀]²

∴ Rate₁/Rate₂ = (k[A₀][B₀]⁰[C₀]²)/(k[1/2A₀][1/2B₀]⁰[1/2C₀]²) = 8.

∴ Rate₂ = 1/8(Rate₁).

So, the rate of the reaction will decrease by a factor of 8.

pre-sliced bread is a relatively recent development in baking technology. previous to that, it was always sold in a bakery in daily-made contiguous loaves with no wrapping, and was moderately perishable, usually being used with a day or two (which is why every bakery had a discounted “day-old” bread table.) therefore, pre-sliced bread would grow stale quickly. the hard crust provided a protective layer, and once the exposed dry slice left from the previous cut was removed, the interior was still soft.

what keeps bread soft is the moisture retained in the crumb (the light spongy part that’s not crust). the reason the crust develops is the surface of the dough gets exposed to hot dry air during baking which browns the outer layer and seals it, preventing all the moisture from escaping the dough. longer exposure to air will also eventually cause your bread to lose flavor and become stale.

people were used to cutting slices as they needed them and storing bread in a specially-made wooden or metal breadbox or pail with a lid to preserve it longer, but the first automatically sliced commercial loaves were produced on july 6, 1928, in chillicothe, missouri, using a machine invented by otto rohwedder, an iowa-born, missouri-based jeweler.[1] pre-sliced bread would indeed dry out, were it not for another 20th century technology: the plastic bag. bread could now be pre-sliced, and if the enclosing bag remains sealed as much as possible, the bread will remain soft and fresh for longer than if sitting unwrapped on a shelf or enclosed in a bread box that is not air-tight. sealed packaging meant bread could also be sold on store shelves and eliminate frequent trips to a bakery.

sealing bread in a plastic bag had another effect: the moisture in the loaf will re-distribute into the crust and soften it, which is sometimes more pleasing in a sandwich - especially for children whose teeth might not yet be strong enough to tear through a hard crust. a homemade loaf of bread can be sealed in a bag overnight and the crust will become soft like store-bought sandwich bread.

these were novel changes in how bread was produced and sold, which led to the coining of the phrase “the greatest thing since sliced bread.”