First you need to find the order of reaction.
Let the reaction follow a simple nth order rate law:
rate = k∙[A]ⁿ
Half-life t₁₂ initial concentration [A]₀ and rate constant k for such a reaction are related as:
t₁₂ = (2ⁿ⁻¹ - 1) / ( (n - 1)∙k∙[A]₀ⁿ⁻¹ )
except the particular case of first order reactions, i.e. n=1, in which half-life does not depend on initial concentration:
t₁₂ = ln(2)/k
Apparently your reaction is not a first order reaction. When you combine the constant factors in the relation above to a constant K, you can see that half-life of a non-first order reaction is inversely proportional to initial concentration raised to the power (n-1):
t₁₂ = K/[A]₀ⁿ⁻¹
with K=(2ⁿ⁻¹ - 1)/((n - 1)∙k)
K cancels out when you take the ratio of the two given half-lifes:
t₁₂₍₂₎ / t₁₂₍₁₎ = (K/[A]₀₍₂₎ⁿ⁻¹) / (K/[A]₀₍₁₎ⁿ⁻¹) = ([A]₀₍₁₎/[A]₀₍₂₎)ⁿ⁻¹
to find the exponent (n-1) take logarithm
ln(t₁₂₍₂₎/t₁₂₍₁₎) = ln(([A]₀₍₁₎/[A]₀₍₂₎)ⁿ⁻¹) = (n - 1)∙ln([A]₀₍₁₎/[A]₀₍₂₎)
=>
n - 1 = ln(t₁₂₍₂₎/t₁₂₍₁₎) / ln([A]₀₍₁₎/[A]₀₍₂₎)
= ln(229s / 151s) / ln(0.297M / 0.196M )
= 1.00198...
≈ 1
=>
n = 2
With known order n we can compute k from given half-life and initial concentration.
For a second order reaction half-life is given by:
t₁₂ = (2²⁻¹ - 1) / ( (2 - 1)∙k∙[A]₀²⁻¹ ) = 1/(k∙[A]₀)
Hence
k = 1/(t₁₂∙[A]₀)
= 1/(151s ∙ 0.297M)
= 2.23×10⁻² M⁻¹s⁻¹
The scientific investigation performed by Elaina is missing control variables.
An ideal scientific investigation should vary only the factor, which is examined, like the volume of the music, while all the other factors should be kept constant.
She hasn't controlled for volume, the volume of the music may influence the rate at which the heart rate of the listener will elevate, in the case, and she should have determined the pulse rate of each individual after the similar rate of listening.
She hasn't controlled for age, as an older person would have reacted to loud music differently from a teenager, that is, all her subjects should be of about the similar age group.
She hasn't controlled for wakefulness, that is, each individual would react to music distinctly when asleep and when is awake.
the answer is c) a mixture that scatters light.
First you have to find the molar mass of the compound. In order to do this, you add together the molar masses of each element in the compound.
Then you divide your starting mass by the molar mass in order to get the amount of moles.
So your answer is 1.5 mols of NaOH