CHM 101/FSC 112: Errors, Accuracy, and Stoichiometry

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Questions and Answers

A student measures the mass of a sample three times and obtains the following values: 15.5 g, 15.6 g, and 15.7 g. The true mass of the sample is known to be 16.8 g. Which statement best describes the student's measurements?

  • Neither accurate nor precise.
  • Accurate but not precise.
  • Both accurate and precise.
  • Precise but not accurate. (correct)

In a laboratory experiment, four students each made three measurements of the length of a metal rod. The actual length of the rod is 25.0 cm. Which student's measurements display both high accuracy and high precision?

  • Student 3: 24.5 cm, 25.5 cm, 26.0 cm
  • Student 4: 26.0 cm, 26.0 cm, 26.0 cm
  • Student 1: 24.8 cm, 24.9 cm, 25.0 cm (correct)
  • Student 2: 25.2 cm, 25.3 cm, 25.1 cm

A chemist performs an experiment to determine the concentration of a solution. Which scenario indicates the presence of systematic error?

  • The chemist's values are inconsistent and show no discernible pattern.
  • The chemist's values are close to each other but fluctuate above and below the true value.
  • The chemist consistently obtains values that are higher than the true value. (correct)
  • The chemist obtains a wide range of values that are randomly scattered around the true value.

A student weighs a sample on a balance and records the mass as 10.25 g. Later, the student discovers that the balance was not calibrated correctly and consistently reads 0.05 g too high. What type of error is this?

<p>Systematic error (B)</p> Signup and view all the answers

What is the term for the extent to which repeated measurements yield the same result?

<p>Precision (B)</p> Signup and view all the answers

In a chemical reaction, the theoretical yield of a product is 25.0 grams. A student performs the reaction and obtains 20.0 grams of the product. What is the percent yield?

<p>80.0% (B)</p> Signup and view all the answers

A chemist measures the mass of a compound to be 5.00 g, but the true mass is 5.20 g. Calculate the absolute error.

<p>-0.20 g (D)</p> Signup and view all the answers

The accepted value for a standard solution's concentration is 0.100 M. A student performs an experiment and obtains a value of 0.095 M. Calculate the percent relative error.

<p>5.0% (D)</p> Signup and view all the answers

A goldsmith weighs a piece of gold and records a weight of 1.45 g, but its actual weight is 1.50 g. Calculate the relative error.

<p>-0.033 (C)</p> Signup and view all the answers

Three students independently perform the same experiment to determine the density of a metal. Their results are: Student 1: 7.85 g/mL, Student 2: 7.88 g/mL, Student 3: 7.82 g/mL. If the true density of the metal is 7.84 g/mL, which statement is most accurate?

<p>The results are both accurate and precise. (C)</p> Signup and view all the answers

What is the purpose of using carbon-12 ($^{12}C$) as the standard for determining relative atomic masses?

<p>It is assigned a mass of exactly 12 atomic mass units, providing a reference for other elements. (C)</p> Signup and view all the answers

Why is the average atomic mass of carbon listed as 12.01 amu on the periodic table, rather than exactly 12 amu?

<p>Carbon exists as isotopes with slightly different masses. (C)</p> Signup and view all the answers

Chlorine has two isotopes: $^{35}Cl$ with a mass of 34.968 amu and $^{37}Cl$ with a mass of 36.956 amu. If the relative abundance of $^{35}Cl$ is 75.77% and $^{37}Cl$ is 24.23%, what is the average atomic mass of chlorine?

<p>35.45 amu (B)</p> Signup and view all the answers

What is the definition of a 'mole' in chemistry?

<p>The amount of a substance that contains as many particles as there are atoms in exactly 12 g of carbon-12. (B)</p> Signup and view all the answers

What is the approximate value of Avogadro's number?

<p>6.022 x 10$^{23}$ (D)</p> Signup and view all the answers

How many hydrogen atoms are present in 0.75 mol of $C_6H_{12}O_6$?

<p>5.42 x 10$^{24}$ (A)</p> Signup and view all the answers

What is the molar mass of methane ($CH_4$)? (Atomic mass: C = 12.01 amu, H = 1.008 amu)

<p>16.04 g/mol (D)</p> Signup and view all the answers

If a sample has a mass of 46 grams and its molar mass is 92 g/mol, how many moles are in the sample?

<p>0.5 moles (A)</p> Signup and view all the answers

What is the percentage composition of carbon in ethanol ($C_2H_5OH$)? (Molar mass: C = 12.01 g/mol, H = 1.008 g/mol, O = 16.00 g/mol)

<p>52.14% (C)</p> Signup and view all the answers

Determine the percentage composition of oxygen in sodium oxalate ($Na_2C_2O_4$). (Molar mass: Na = 22.99 g/mol, C = 12.01 g/mol, O = 16.00 g/mol)

<p>59.43% (B)</p> Signup and view all the answers

Which of the following is a valid unit for molar mass?

<p>grams per mole (C)</p> Signup and view all the answers

A reaction requires 2.0 moles of reactant A (molar mass = 50 g/mol). What mass of reactant A is needed?

<p>100 g (D)</p> Signup and view all the answers

Given the reaction: $2H_2 + O_2 → 2H_2O$. If 4.0 grams of $H_2$ react completely, how many grams of $H_2O$ are produced? (Molar mass: $H_2$ = 2.0 g/mol, $H_2O$ = 18.0 g/mol)

<p>36.0 g (D)</p> Signup and view all the answers

Consider the following balanced equation: $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$. If you start with 6.022 x $10^{23}$ molecules of $N_2$, how many molecules of $NH_3$ can be produced, assuming excess $H_2$?

<p>1.2044 x $10^{24}$ (C)</p> Signup and view all the answers

For the reaction $2CO(g) + O_2(g) \rightarrow 2CO_2(g)$, if you have 4 moles of CO and 3 moles of $O_2$, which reactant is the limiting reactant?

<p>CO (B)</p> Signup and view all the answers

In the reaction $A + 2B \rightarrow C$, if the molar mass of A is 20 g/mol and the molar mass of B is 10 g/mol, what mass of B is required to completely react with 10 g of A?

<p>10 g (B)</p> Signup and view all the answers

A compound is found to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. What is its empirical formula?

<p>$CH_2O$ (A)</p> Signup and view all the answers

A compound has an empirical formula of $CH_2O$ and a molar mass of 180 g/mol. What is its molecular formula?

<p>$C_6H_{12}O_6$ (A)</p> Signup and view all the answers

If 5.0 g of methane ($CH_4$) is completely combusted, what mass of carbon dioxide ($CO_2$) is produced? (Molar mass: CH4 = 16 g/mol, CO2 = 44 g/mol)

<p>13.8 g (B)</p> Signup and view all the answers

Consider the reaction: $2A + B \rightarrow C$. If 100 g of A (molar mass 25 g/mol) reacts with 80 g of B (molar mass 40 g/mol), which reactant is limiting?

<p>A (D)</p> Signup and view all the answers

If the percentage composition of hydrogen in a compound is 2.016%, and the molar mass of the compound is 100 g/mol, what is the mass of hydrogen in one mole of the compound?

<p>2.016 g (A)</p> Signup and view all the answers

In mass spectrometry, what causes ions with lower molecular weight to deflect more than ions with higher molecular weight?

<p>Their interaction with the magnetic field (A)</p> Signup and view all the answers

Using the diagram showing targets, which of the following best describes 'Jane's' shooting?

<p>Accurate but not precise (C)</p> Signup and view all the answers

What distinguishes relative error from absolute error in measurements?

<p>Relative error accounts for the size of the true value, while absolute error does not. (B)</p> Signup and view all the answers

Why is it important to distinguish between accuracy and precision in scientific measurements?

<p>Distinguishing them helps in identifying sources of error and improving experimental techniques. (A)</p> Signup and view all the answers

How does the mass spectrometer differentiate between isotopes of the same element?

<p>By ionizing and separating them based on their mass-to-charge ratio. (C)</p> Signup and view all the answers

Flashcards

What is error in measurement?

Difference between observed/measured value and true value.

What is relative error?

Error expressed as a fraction of true value.

What is Accuracy?

Closeness of measurement to true value.

What is Precision?

Extent to which repeated measurements agree.

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What is Stoichiometry?

Quantities of materials consumed/produced in reactions.

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What is relative atomic mass?

Mass of an atom relative to Carbon-12.

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What is average atomic mass?

Weighted average of isotopes' atomic masses

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What is a mole?

The amount of substance containing Avogadro's number of particles.

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What is Avogadro's number?

6.022 x 10^23, the number of entities in one mole.

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What is molar mass?

Mass of one mole of a substance.

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What is percentage composition?

Determining mass ratios and % of elements in compounds.

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Study Notes

CHM 101/FSC 112 Topics

  • Covers errors, accuracy, and precision
  • Explores stoichiometry

Intended Learning Outcomes

  • Ability to measure error
  • Ability to explain accuracy and precision
  • Understanding and application of the Mole concept to calculations

Errors in Measurements

  • All measurements involving a numerical answer include some degree of error.
  • Errors come from the instruments and/or personal errors when analysts fail to accurately read instruments
  • Measurement error is the difference between the observed/measured value and the true value
  • Also known as the absolute error: Absolute error = measured value - true value

Relative Error

  • Errors can be expressed as relative error and percentage relative error
  • Relative error = absolute error/true value
  • % relative error = |absolute error|/true value x 100

Accuracy and Precision

  • Accuracy is the degree of agreement between the measured value and the true value
  • Precision is the extent to which results agree with one another, or repeatability of a result

Example To Determine Accuracy and Precision

  • Student A's measurements: 1.964 g, 1.978 g, 1.960 g
  • Student B's measurements: 1.968 g, 1.969 g, 1.973 g
  • Student C's measurements: 2.001 g, 2.002 g, 2.003 g
  • True value: 2.000g
  • Student C is the most accurate and precise

Stoichiometry

  • Deals with the quantities of materials/substances consumed (reactants) and produced (products) in chemical reactions
  • Understanding this requires understanding of certain concepts

Relative Atomic Masses

  • Atoms, being very small, cannot be weighed individually, making it impossible to weigh a single atom
  • The mass of an atom can only be determined relative to another experimentally
  • Carbon 12 is the standard, with a mass of exactly 12 atomic mass units and provides the standard for measuring atomic mass of other elements

Average Atomic Mass

  • Atomic mass of carbon is 12.01 instead of 12.00 due to isotopes i.e two atoms having the same atomic number but different mass number)
  • The average atomic mass can be calculated using the relative abundance

Average Atomic Mass Example

  • Carbon-12 has a relative abundance of 98.89%
  • Carbon-13 has a relative abundance of 1.11%

Avogadro's Number and the Mole

  • A mole is the amount of substance containing as many atoms, molecules, or other particles as there are in exactly 12 g of carbon-12
  • Samples have multiple atoms, a "mole" has been established to measure them
  • Equal to the number of carbon atoms in exactly 12 g of pure Carbon-12
  • 12 g of Carbon-12 contains 6.023 x 10e23 atoms
  • 6.023 x 10e23 = Avogadro's Number

Examples of Moles

  • 1 mole of Carbon-12 = 6.023 x 10e23 atoms
  • 1 mole of Hâ‚‚O molecules = 6.023 x 10e23 Hâ‚‚O molecules
  • 1 mole of NO3- ions = 6.023 x 10e23 NO3- ions
  • 1 mole of H atoms = 6.023 x 10e23 atoms
  • 1 mole of O atoms = 6.023 x 10e23 atoms
  • 1 mole of Hâ‚‚ molecules = 6.023 x 10e23 molecules

The Molar Mass

  • The mass (in grams) of one mole of a compound
  • Determined by summing the atomic masses of all component atoms

Molar Mass Examples

  • One mole of Magnesium atom = 24.31 g - molar mass is 24.31 g/mol
  • Molar mass of methane (CH4) is CH4 = (12.01 x 1) + (1.008 x 4) = 16.04 g/mol

Molar Mass Formula

  • No of moles = mass / molar mass

Percentage Composition of Elements

  • To determine the percentage composition of elements in a compound, determine molar mass of compound, then determine the mass ratios and percent

Percentage Composition Example

  • Determine the percentage composition of ethanol (C2H5OH)
  • % C = 52.13%, % H = 13.15%, % O = 34.72%
  • Determine the percentage composition of sodium oxalate (Na2C2O4)
  • % Na = 34.31%, % C = 17.93%, % O = 47.76%

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