Quant Chem 1st midterm

quantitative calculations, definitions, theories

SI Units for length

meter (m)

SI Units for mass

kilogram (kg)

SI Units for time

second (s)

SI Units for Temperature

kelvin (K)

SI Units for amount of substance

mole (mol)

SI Units for electric current

ampere (A)

What is the Symbol and factor for deca?

da, $10^1$

What is the Symbol and factor for kilo?

k, $10^3$

What is the Symbol and factor for deci?

d, $10^{-1}$

What is the Symbol and factor for micro?

$$\text{μ}, \, 10^{-6}$$

Which of these prefixes represents the smallest factor of 10?

pico

What is the Symbol and factor for pico?

$$\text{p}, \, 10^{-12}$$

What is the Symbol and factor for giga?

$$\text{G}, \, 10^{9}$$

What is the Symbol and factor for nano?

$$\text{n}, \, 10^{-9}$$

The value 3.5*$10^{-5}$ A is equal to what?

35μA

A car is driving at 65 miles per hour (mi/h). What is the speed of the car in kilometers per second (km/s)? 1 mi =1.609 km

$\frac{65 \times1.609}{3600}\text{ km/s}$ =$\text{2.9}\cdot\text{10}^{\text{-2}}$ km/s

Which of these is not equal to the formal concentration of a substance?

total ion concentration

The density of 70.0 wt% ACS reagent grade HClO₄ (FM 100.46) is 1.664 g/mL. Calculate the molarity.

To calculate the molarity, use the formula $\text{M} = \frac{\text{density} \times \text{wt\text{ }\text{percent}}}{\text{FM} \times 1000}$, which results in a molarity of approximately 11.1 M.

The concentration of a 1 ppb dilute aqueous solution can be expressed as

1 ng/mL

Anhydrous acetonitrile contains less than 0.001 wt% water. Express the water impurity in ppm.

10 ppm

What is the concentration (in ppm) of Cu2+ (FM  63.546) in a 2.7 × 10−4 M aqueous CuSO4 (FM 159.602) solution? 

To calculate the concentration of Cu$^{2+}$ in ppm, use the formula $\text{ppm}=\text{Molarity}\times\text{FM}\times1000$ . This results in a concentration of approximately 17ppm.

Phenol (analytical standard) is available as a 5000. μg/mL solution in methanol. What aliquot do you have to take to make 25.0 mL of a 100. μg/mL solution?

V1 = $\frac{C2 \times V2}{C1} \, = \frac{100 \, \text{µg/mL} \times 25.0 \, \text{mL}}{5000 \, \text{µg/mL}}$ = 0.500mL. You need to convert to μL by multiplying by 1000 = 500 μL

Lead(II) chloride precipitates when a solution of Pb2+ and a solution of Cl− are mixed together. If you mix 100 mL of a 0.205 M Pb2+ solution with 150 mL of a 0.245 M Cl− solution, what is the limiting reagent?

The limiting reagent can be determined by calculating the moles of Pb$^{2+}$ and Cl$^{-}$ in the mixed solutions. To caculate for mol of Pb$^{2+}$, use the formula: $\text{moles} = \text{concentration} \times \text{volume}$. This gives you moles of Pb$^{2+}$ as 0.205 M × 0.100 L = 0.0205 moles. For Cl$^{-}$: 0.245 M × 0.150 L = 0.03675 moles. Based on the chemical equation there are 2Cl for every Pb so 0.03675 moles is divided by 2. This makes the limiting reagent Cl^-

Which Class A buret has the lowest relative uncertainty?

50mL buret

Round 0.600 43 to three significant figures

0.600

Identify the answer with the correct number of significant figures. 4.59 g – 26.143 3 g = ?

-21.55g

Identify the answer with the correct number of significant figures. log(3.456 × 10⁷) = ?

7.5386

Which of the following is NOT a characteristic of random (or indeterminate) error?

It arises from a flaw in equipment or the design of an experiment

A systematic error can be corrected by

proper calibration and consistent measurement techniques.

The final buret reading is 24.40 ± 0.02 mL and the initial buret reading is 0.05 ± 0.02 mL. What is the uncertainty in the volume delivered?

± 0.03 mL

Formula for experimental uncertainty

e = square root of the sum of the squares of the individual uncertainties.

what fraction of the measurement values are expected to lie within plus or minus one standard deviation (±1σ) for a set of data that exhibits a Gaussian distribution?

0.682

What is the Emperial Rule?

The Empirical Rule states that for a normal distribution, approximately 68% of data falls within one standard deviation (±1σ) from the mean, about 95% within two standard deviations (±2σ), and about 99.7% within three standard deviations (±3σ).

True or False: A standard deviation close to zero means that the data points are close to the mean of the set.

True

When F_calculated is greater than F_table at the 95% confidence level, there is a less than 5% chance that the two data sets come from the same populations with the same population standard deviation.

True. This indicates that there is significant evidence to reject the null hypothesis in hypothesis testing.

Under the circumstance of measuring the same sample, the wider the confidence interval is, the lower the probability that the measured value lies within the confidence interval.

False

A t test can be used to compare results (averages) from two different methods. If the difference in the results is significant, it means that

there is a systematic error in at least one of the methods

Sensitivity is

measured by the slope of the calibration curve.

Selectivity is the extent to which a method is reproducible by different people with different equipment to get the same results.

False

Caffeine was analyzed using UV-Vis spectroscopy. The average absorbance for 10 blanks is 0.018 26. The standard deviation from the measurement of seven samples with a concentration about three times the detection limit is 0.003 4. The slope of the calibration curve is 1.75 × 109 M−1. Calculate the signal detection limit.

0.028 because y_{detec. limit} = y_blank *3 (standard deviation of detec. limit)

The absorption of seven replicate samples with concentrations about three times the detection limit was measured. The slope of the calibration curve was 0.356 mM⁻¹. The standard deviation of the absorption measurements was 0.67. Calculate the detection limit.

LOD = 3s/m where LOD is the limit of detection, s is the standard deviation of the blank samples, and m is the slope of the calibration curve. (2.80)

A solution containing 2.0 wt% X (analyte) and 3.5 wt% S ( internal standard) gave peak areas of 38 234 and 23 880 for the analyte and standard, respectively. Calculate the response factor.

The response factor (RF) is calculated as RF = (Area of X/ Area of S)*( concentration of S/ Concentration of X), where A is the peak area and C is the concentration.

A set of five solutions are prepared by delivering 10 mL of unknown sample and increasing volumes of standard (0, 5, 10, 15, and 20 mL) into 50-mL volumetric flasks. Analytical reagents are then added and the flasks are diluted to volume. The x-intercept of the best-fit line is −5.63 mM. What is the concentration of the unknown?

28.2mM

How does an electronic Balance work?

By measuring the electromagnetic force needed to counteract the weight of an object placed on it. A load cell detects the force and sends an electronic signal to a display, showing the weight.

How do you minimize erros on a electronic balance?

Keep the balance on a leveled surface, measure sample close to the center of the balance, keep in an ambient temperature, close the glass doors, and avoid fingerprints with gloves or tweezers.

what are hygroscopic reagents?

Reagents that readily absorb moisture from the air, often used to maintain dryness in chemical reactions or experiments.

What is the relation between glassware and relative uncertainty?

The larger the volumetric glassware, the smaller its relative uncertainty.

How do you calculate percent relative uncertainty?

% relative uncertainty = ( uncertainty in quantity) / (magnitude of quantity) * 100%

How do you write the equilibrium constant K for a reaction? A^a + B^b → C^c + D^d

K =[C^c][D^d ]/[A^a][B^b]

What is the value of L when the reaction if favors?

K>1 indicates that the products are favored at equilibrium.

Manipulate equilibrium constants

review

How do you calculate Gibbs free energy change under non standard conditions?

$\Delta G = \Delta G^\circ + RT \ln Q$ and at equilibrium $Q = K$ and thus $\Delta G = 0$. So the equation becomes $\Delta G^{\circ}=-RT\ln K$

What is the value of the gas constant R

$$8.314 \frac{J}{mol \times K}$$

When is a reaction favored or unfavored based on K and $\Delta G^{\circ}$ ?

A reaction is favored when $\text{K} > 1$, indicating that products are favored at equilibrium, while it is unfavored when $\text{K} < 1$, meaning reactants are favored. Correspondingly, if $\text{ΔG}^\text{°} < 0$, the reaction is spontaneous and favored, whereas $\text{ΔG}^\text{°} > 0$ suggests it is non-spontaneous and unfavored.

Think for K arrow points towards favoritism and opposite for $\Delta G^{\circ}$

What are some rules for writing equilibrium constants?

Solids and pure liquids are omitted from the expressions.

Define Solubility Product (K_sp )

The solubility product constant (Ksp) is an equilibrium constant that describes the extent to which a sparingly soluble ionic compound dissolves in water, represented as the product of the molar concentrations of its constituent ions, each raised to the power of their stoichiometric coefficients.

What is the definition of Bronsted-Lowry Acids and Bases?

Bronsted-Lowry acids are substances that donate protons (H+ ions), while Bronsted-Lowry bases are substances that accept protons.

What is the equilibrium constant of water?

$K_w$= $1.0 \times 10^{-14}$.

Can strong acids and strong bases have an equilibrium constant?

Strong acids and strong bases are considered to completely dissociate in solution, making their equilibrium constants effectively infinite or not applicable in typical contexts.
K_a K_b →∞

Memorize

Memorize

What are the most common weak acids and bases?

carboxylic acids (RCO₂H) and for bases: amines (R₃N)

What is titration?

Titration is a laboratory technique used to determine the concentration of a substance in a solution by reacting it with a reagent of known concentration, typically involving a color change at the endpoint.

or a titrant (standardized) is added to an unknown solution of analyte until the analyte is exactly consumed by the reaction,

What is the diffrence between equivalence point and end point?

The equivalence point is the point in a titration at which the amount of titrant added is exactly enough to completely neutralize the analyte, while the endpoint is the point at which the indicator shows that the equivalence point has been reached, usually through a visible change.

Exact vs visible.

What is back titration?

Back titration is a technique used when the analyte is not directly titratable, where an excess of titrant is added to react with the analyte, and then the unreacted titrant is titrated with a second standard solution to determine the amount of analyte.

pX = - log [X] wht happens at high volumes of x

At high volumes of X, the concentration approaches zero, leading to a decrease in pX values, indicating increased acidity or basicity depending on the nature of X.

What is the formula for Standard deviation of a sample?

 Sample Standard deviation:

Definition of 1 ppm for aqueous solutions

1ppm = 1mg/L = 1$\mu$g/mL = 1$\mu$g/g = 1mg/kg (assuming solution densoty = 1g/mL)

Definition of 1 ppb for aqueous solutions

1ppb = 1$\text{µg/L}$ = 0.001$\text{mg/L}$ = 1$\text{µg/mL}$ = 1$\text{µg/g}$ = 1$\text{mg/kg}$ (assuming solution density = 1$\text{g/mL}$)

Formula to convert mass percent (%w/w) to Molarity (M)

Molarity $(M)=\frac{\left(mass\;percent\;\times\;density\;of\;solution\left(\frac{g}{mL}\right)\right)\cdot10}{\left(molar\;mass\;of\;solute\;\left(\frac{g}{mol}\right)\right)}$

Formula to convert ppm to Molarity (M)

Molarity $(M)=\frac{ppm\times\frac{1g}{1000mL}}{molar\;mass\;of\;solute\;\left(\frac{g}{mol}\right)}$

Stoichiometry calculation vs Dilution formula usage?

Stoichiometry calculations involve using balanced chemical equations to determine the relationships between reactants and products, while dilution formulas are used to calculate concentrations after a solvent has been added to a solution.

Absoulte uncertainty vs relative uncertainty

Absolute uncertainty refers to the uncertainty of a measurement expressed as a specific quantity,

whereas relative uncertainty is the absolute uncertainty divided by the measured value, often expressed as a percentage or fraction of the measurement.

Error propagation rule for addition and subtraction

for y- a+b - c the absolute uncertainties are added:
e_y = $\sqrt{(e_{_{}a}^{})^2+(e_{b})^2+(e_{c})^2}$

error propagation rule for multiplication and division

e_y /y = $\sqrt{(\frac{e_{_{}a}^{}}{a})^2+(\frac{e_{b}}{b})^2+(\frac{e_{c}}{c})^2}$

Population parameters vs Sample statistics

Population parameters ( $\mu$, $\sigma$ ) represent the true infinite set.
Sample statistics ( avg{x} , $s$) are estimates derived from a finite subset of the population.

Formula for Confidene Interval (CI) using t-distribution)

CI = avg X + or - (t*s)/ squart root of n . where t is the Student’s t value for degrees of freddom df= n-1

Limit of Quantification

The lowest concentration of an analyte that can be reliably measured, the formula is 10s_blamk /m

Define Gravimetric Analysis principle

A method of measuring the quantity of an analyte based on its mass, typically involving precipitation and filtration.

Equilibrium Constant (K) vs Reaction Quotient (Q)

The equilibrium constant (K) is a ratio that expresses the concentrations of products to reactants at equilibrium,

while the reaction quotient (Q) is the same ratio but for concentrations at any point in time, indicating the direction of the reaction.

Decision rule for Student’s t-test

If t_calc > t_table, the difference is statistically significant at the chosen confidence level (reject null hypothesis).

Limit of Determination

Lod = 3_blank /m, where s_blank is the blank standard deviationand m is the calibration curve slope.

Fractional Precipitation: quantitative seperation criterion

Seperation is considered quantitative if greater than or equal to 99.9% of the first metal precipitates before the second metal begins to precipitate.

Condition rquired for precipitation to occur.

Precipitation begins when the reaction quotient Q_sp >_ K_sp

Water Ion Product (K_w )

$K_w = [H^+][OH^-]$ at $25^\text{°C}$
= $1.0 \times 10^{-14}$

If F_calculated = (s1)^2/ (s2)^2 > F_table what is determined about the null hypothesis?

The null hypothesis is rejected, indicating significant differences between the groups.