Measurements - AP Chemistry

Card 0 of 336

Question

What is the concentration of Ca in a solution of 1 mol CaCl2 in 1 L of distilled water? (M = molarity, m= molality)

Answer

The definition of molality is moles of solute in 1 kg of the solvent, whereas molarity is the number of moles of solute per 1 L of solutioin. Since 1 mol of CaCl2 is added to 1 L of water, this means that the volume of the final solution is greater than 1 L. Thus, molality is the more accurate concentration determinant, since the solution is probably close to 1 L.

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Question

Which of the following is equivalent to molarity?

Answer

Molarity, molality, and normality are the three principle ways to measure concentration. Molarity is a measure of moles of solute per liter of solution. Molality is a measure of moles of solute per kilogram of solvent. Normality expressly relates to acids and bases, and is the measure of moles of solute divided by the number of hydrogen equivalents per mole, all divided by liters of solution. Normality is also referred to as "equivalents (of acid) per liter."

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Question

How many moles of are in of a solution?

Answer

Molarity is defined as moles of solute divided into liters of solution. We can set up the equation as follows:

$0.1M = \frac{x}{5 L}$

Set the left side of the equation over and solve as a proportion.

$\frac{0.1M}{1} = \frac{x}{5 L}$

Cross multiply.

Remember molarity is defined as moles of solute per liter of solution.

$M=\frac{mol}{L}$

Substiute.

$x=\frac{0.1mol}{L}*\frac{5L}{1}$

Liters cancel out.

Solve for the number of moles. This gives us of solute in a , solution of .

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Question

Which of the following units is common for measuring concentration?

Answer

$\frac{mol}{L}$ is the dimensional breakdown for the commonly used unit , or molarity, for concentration.

While the other units might be seen in chemistry, they are used for other topics.

Millimeters of mercury (mmHg) and atmospheres (atm) are seen in regards to pressure.

$\frac {kg}{m^3}$ is the dimensional breakdown for density. And $\frac{kg \cdot m}{s^2}$ is the dimensional breakdown for a Newton, also written as N. This is associated with force.

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Question

How many atoms are in 1 mole of H2?

Answer

This question requires an understanding of what avogadro's number actually represents. Avogadro's number, 6.022 * 1023 is the number of things in one mole. The question indicates that there is 1 mole of H2. Thus there are 6.022 * 1023 molecules of H2. However the question is asking for the amount of atoms in 1 mole of H2. Thus we must consider the makeup of an H2 molecule, where we see that it is a diatomic molecule. Thus we must multiply 6.022 * 1023 by 2 to calculate the number of individual atoms present in 1 mole of H2. We find our answer to be 1.2044 * 1024.

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Question

A chemist has $4.37*10^{-3}g$ of $CH_3CH_2OH$ .

How many molecules of $CH_3CH_2OH$ does she have?

Answer

$4.37\times 10^{-3}g\hspace{1 mm}CH_3CH_2OH\times \frac{1\hspace{1 mm}mole\hspace{1 mm}CH_3CH_2OH}{46\hspace{1 mm}g\hspace{1 mm}CH_3CH_2OH}\times\frac{6.022\times 10^{23}\hspace{1 mm}molecules\hspace{1 mm} CH_3CH_2OH}{1\hspace{1 mm}mole\hspace{1 mm}CH_3CH_2OH}=5.72\times10^{19}\hspace{1 mm}molecules\hspace{1 mm}CH_3CH_2OH$

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Question

What is the mass of $5.34\times10^{15}$ particles of $C_2H_6$ ?

Answer

$5.34\times10^{15}\hspace{1 mm}particles\hspace{1 mm}C_2H_6\times \frac{1\hspace{1 mm}mole\hspace{1 mm}C_2H_6}{6.022\times 10^{23}\hspace{1 mm}particles\hspace{1 mm} C_2H_6}\times \frac{30.0\hspace{1 mm}g\hspace{1 mm}C_2H_60=}{1\hspace{1 mm}mole\hspace{1 mm}C_2H_6}=2.66\times 10^{-7}g\hspace{1 mm}C_2H_6$

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Question

How many atoms are in $\small 50g$ of calcium?

Answer

In order to determine how many atoms are in this sample, we need to convert this sample into moles. Calcium has a molar mass of $\small 40.08$ grams per mole.

$50g\ Ca\frac{1mol\ Ca}{40.08g\ Ca}=1.25mol\ Ca$

Avogadro's number tells us that there $6.02210^{23}$ atoms in one mole of any element. We can use this conversion to find the total number of atoms in the sample.

$1.25 moles* \frac{6.02210^{23}atoms}{1mol} = 7.510^{23} atoms$

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Question

How many hydrogen atoms are in 46.3 g of ethanol, ?

Answer

To determine the number of hydrogen atoms, divide the mass of ethanol by its molar mass to get moles of ethanol.

$MM=(12)+6(1)+(16)=34\frac{g}{mol}$

$46.3g\frac{1mol}{34g}=1.36mol\ CH_6O$

Multiply this by six atoms of hydrogen per molecule of ethanol and by Avogadro's number to get the number of hydrogen atoms.

$1.36mol\ CH_6O\frac{6mol\ H}{1mol\ CH_6O}=8.17mol\ H$

$8.17mol\ H\frac{6.02210^{23}\text{atoms}}{1mol}=4.9*10^{24}\text{atoms}$

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Question

How many hydrogen atoms are present in 500 mL of water at room temperature?

$\rho_{\text{water}}=1\frac{g}{mL}$

Answer

Use the density of water, the molar mass of water, and Avogadro's number to calculate the number of molecules of water.

We have 500mL of water. Use the density to convert this to grams; then use the molar mass of water to convert this to moles.

$500mL\frac{1g}{1mL}\frac{1mol}{18g}=27.78mol\ H_2O$

There are two moles of hydrogen atoms per one mole of water.

$27.78mol\ H_2O\frac{2mol\ H}{1mol\ H_2O}=55.56mol\ H$

Finally, multiply by Avogadro's number.

$55.56mol\ H\frac{6.02210^{23}\text{atoms}}{1mol}=3.3510^{25}\text{atoms}$

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Question

How many molecules are in ?

Answer

According to Avogadro's law, each mole of a compound contains $6.02\cdot10^{23}\text{molecules}$ . Use dimensional analysis to find the number of molecules in .

$5.2mol: KCl\cdot \frac{6.02\cdot 10^{23}\text{molecules}}{1mol}=3.13\cdot10^{24}\text{molecules}$

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Question

How many atoms are there in 47.5g of boron?

Answer

To do this problem we have to first convert grams to moles, then moles to atoms using Avogadro's number:

$47.5g\frac{1mol\ B}{10.8g\ B}\frac{6.02210^{23}\ \text{atoms}}{1mol}=2.6510^{24}\text{atoms}$

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Question

How many moles of carbon are in a sample of $25.125*10^{27}$ atoms?

Answer

To solve, we need to convert atoms to moles using Avogadro's number:

$25.12510^{27}\text{atoms}\frac{1mol}{6.02210^{23}\text{atoms}}=4.1710^4mol$

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Question

How many atoms of sodium are in three moles of $Na_{2}S$ ?

Answer

To answer this question, we have to find the number of moles of sodium in this compound. Note that there are two sodium atoms per molecule. Then, multiply the total moles of sodium by Avogadro's number.

$3 mol\ Na_{2}S\frac{2mol\ Na}{1 mol\ Na_{2}S}\frac{6.02210^{23}\text{atoms\ Na}}{1 mole\ Na}=3.6110^{24}\text{atoms Na}$

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Question

You have a neutral balloon. If you were to add 21,000 electrons to it, what would its net charge be?

$e=1.6\cdot 10^{-19}$ = charge of one electron

Answer

The elemental charge is the magnitude of charge, in Coulombs, that each electron or proton has. Because electrons have a negative charge, don't forget to add a negative sign into the equation.

$q=-(#\ of\ electrons)(e)$

$q= -(21000)(1.6\cdot 10^{-19})$

$q= -3.36\cdot 10^{-15}$

When you convert the answer to microcoulombs, the answer is $-3.36\cdot 10^{-9}\mu C$ :

$-3.36\cdot 10^{-15} C\cdot\frac{1.0\cdot10^6 \mu C}{1 C}= -3.36\cdot 10^{-9}\mu C$

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Question

Determine the number of sodium atoms in a block of sodium chloride.

Answer

Use dimensional analysis:

$150gNaCl\frac{1molNaCl}{58.44gNaCl}\frac{1 mol Na}{1 mol NaCl}\frac{6.0210^{23}atoms}{1 mol}=1.55*10^{24}atoms$

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Question

A container has $4.33\times 10^{24}$ molecules of gas in it. How many moles of the gas are in the container?

Answer

Avogadro's number tells us how many molecules of gas are in one mole of the container. We are essentially doing a unit conversion from "number of molecules" to moles -

$4.33\times 10^{24} molecules\left ( \frac{1 mole}{6.022\times 10^{23} molecules} \right )=7.19 moles$

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Question

Consider the following four samples:

$\small 50g$ of potassium

$\small 50g$ of lithium

$\small 50g$ of magnesium

$\small 50g$ of chlorine gas

Which of the given samples contains the most atoms?

Answer

It is important to note that the mass of a sample does not tell you the amount of atoms in the sample. The number of atoms in a sample is dependent on the number moles in a sample, given by Avogadro's number. Here is the number of moles for each sample:

$50 g\ Li\frac{1 mol\ Li}{6.94 g\ Li} = 7.2 mol\ Li$

$50 g\ Mg\frac{1 mol\ Mg}{24.31 g\ Mg} = 2.1 mol\ Mg$

$50 g\ K\frac{1 mol\ K}{39.10 g\ K} = 1.3 mol\ K$

$50 g\ Cl_2\frac{1 mol\ Cl_2}{70.90 g\ Cl_2} = 0.71 mol\ Cl_2$

Remember that chlorine is a diatomic mass, so each molecules contains two atoms. This doubles the molar mass for the conversion.

The sample with the greatest number of moles will also contain the most atoms. In this case, the sample of lithium results in the largest number of moles and, thus, the greatest number of atoms.

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Question

Convert the following amount from grams (g) to moles (m)

How many moles is of ?

Answer

Use the periodic table to calculate the molecular weight of sodium hydroxide.

$MW_{NaOH}= 39.99\frac{g}{mol}$

Next, use dimensional analysis to find the number of moles.

$357g:NaOH\cdot\frac{1mol}{39.99g}=8.93mol$

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Question

$2KBr\ +\ Cl_2\ \rightarrow\ 2KCl\ +\ Br_2$

Consider the reaction above. If you start with of potassium bromide, how many moles of bromine are produced? How many molecules is this equal to?

Answer

In the chemical equation, the ratio of potassium bromide to bromine is 2:1, so for every 2 moles of , 1 mole of is produced. Therefore, if we start with 4 moles of , we get 2 moles of . The number of molecules is equal to the number of moles times Avogadro's Number. Since we've determined the number of moles to be 2, the number of molecules is:

$2\cdot 6.02\cdot 10^{23}=1.204\cdot10^{24}molecules$

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