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wolverine [178]
2 years ago
5

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with mean = 110 grams and standard deviation =

25 grams. What is the probability that a randomly selected vitamin will contain between 82 and 100 grams of pyridoxine?
Chemistry
1 answer:
KIM [24]2 years ago
5 0

Answer:

0.21108

Explanation:

Given,

Mean,

\mu = 110\text{ gram}

Standard deviation,

\sigma = 25\text{ gram}

Let X represents the amount of pyridoxine contained by vitamin,

So, the probability of vitamin will contain between 82 and 100 grams of pyridoxine,

= P( 82 ≤ X ≤ 100 )

P(\frac{82-\mu}{\sigma}\leq \frac{X-\mu}{\sigma}\leq \frac{100-\mu}{\sigma})

P(\frac{82 - 110}{25}\leq z \leq \frac{100-110}{25})

P(-1.12\leq z\leq -0.4)

P(z\leq -0.4)-P(z\leq -1.12)

=0.34458-0.13350

= 0.21108

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The measurement of Rachel’s group is precise but not accurate while the measurement of Ashley’s group is accurate but not precise.

Precision has to do with how close together the values obtained from a scientific measurement is. If we take a look at the values obtained by  Rachel’s group, we will notice that the values are exactly 1.00 g apart. This means that the values are precise.

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The values obtained by Ashley’s group do not have consistent intervals therefore, they are not precise.

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A sample of gold (Au) has a mass of 45.39 g.
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<span>1. What is the molar mass of gold?
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</span><span>2. Calculate the number of moles of gold (Au) in the sample. Show your work. 
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For 45.39 grams of gold, the number of moles would be:
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3. Calculate the number of atoms of gold (Au) in the sample. Show your work.Moles is unit of a number of molecules but 1 mol doesn't represent 1 molecule. The number of atoms can be obtained by multiplying the number of moles with Avogadro number. The calculation would be:
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A weather balloon is filled with helium that occupies a volume of 5.57 104 L at 0.995 atm and 32.0°C. After it is released, it r
Alchen [17]

6.52 × 10⁴ L. (3 sig. fig.)

<h3>Explanation</h3>

Helium is a noble gas. The interaction between two helium molecules is rather weak, which makes the gas rather "ideal."

Consider the ideal gas law:

P\cdot V = n\cdot R\cdot T,

where

  • P is the pressure of the gas,
  • V is the volume of the gas,
  • n is the number of gas particles in the gas,
  • R is the ideal gas constant, and
  • T is the absolute temperature of the gas in degrees Kelvins.

The question is asking for the final volume V of the gas. Rearrange the ideal gas equation for volume:

V = \dfrac{n \cdot R \cdot T}{P}.

Both the temperature of the gas, T, and the pressure on the gas changed in this process. To find the new volume of the gas, change one variable at a time.

Start with the absolute temperature of the gas:

  • T_0 = (32.0 + 273.15) \;\text{K} = 305.15\;\text{K},
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The volume of the gas is proportional to its temperature if both n and P stay constant.

  • n won't change unless the balloon leaks, and
  • consider P to be constant, for calculations that include T.

V_1 = V_0 \cdot \dfrac{T_1}{T_2} = 5.57\times 10^{4}\;\text{L}\times \dfrac{258.65\;\textbf{K}}{305.15\;\textbf{K}} = 4.72122\times 10^{4}\;\text{L}.

Now, keep the temperature at T_1 =258.65\;\text{K} and change the pressure on the gas:

  • P_1 = 0.995\;\text{atm},
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The volume of the gas is proportional to the reciprocal of its absolute temperature \dfrac{1}{T} if both n and T stays constant. In other words,

V_2 = V_1 \cdot\dfrac{\dfrac{1}{P_2}}{\dfrac{1}{P_1}} = V_1\cdot\dfrac{P_1}{P_2} = 4.72122\times 10^{4}\;\text{L}\times\dfrac{0.995\;\text{atm}}{0.720\;\text{atm}}=6.52\times 10^{4}\;\text{L}

(3 sig. fig. as in the question.).

See if you get the same result if you hold T constant, change P, and then move on to change T.

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