Measurement and Data Processing

How should a measurement of $5.00\text{ g}$ be reported if the balance has an absolute uncertainty of $\pm 0.01\text{ g}$?

A student finds the experimental value of $R$ to be $8.41\text{ J K}^{-1}\text{ mol}^{-1}$. If the accepted value is $8.31\text{ J K}^{-1}\text{ mol}^{-1}$, what is the percentage error?

Which of the following is the most appropriate instrument to measure exactly $25.00\text{ cm}^3$ of a solution?

If the length of a side of a square is $10.0 \pm 0.2\text{ cm}$, what is the percentage uncertainty in its area?

The density ($\rho$) of a cylindrical metal rod is calculated using the formula $\rho = \frac{m}{\pi r^{2} l}$, where $m$ is mass, $r$ is radius, and $l$ is length. The percentage uncertainties for the measurements are provided in the diagram. Assuming $\pi$ is an exact value, what is the total percentage uncertainty in the calculated density?

A student measures the distance a trolley travels as $2.50 \pm 0.05$ m. What is the absolute uncertainty in the distance if they double the measured distance?

Which of the following is true regarding significant figures in logarithms (e.g., pH)?

A student determines the volume of metal in a hollow cylindrical pipe by measuring its length ($h$), the external radius ($R$), and the internal radius ($r$). The measurements obtained are:

$h = 10.0 \pm 0.1$ cm $R = 5.0 \pm 0.1$ cm $r = 4.0 \pm 0.1$ cm

The volume of the metal is calculated using the formula $V = \pi h (R^{2} - r^{2})$. Following the standard IB rules for the propagation of uncertainties, what is the absolute uncertainty in the calculated volume, in $cm^{3}$?

Which statement about significant figures is correct during the calculation of $pH = -\log[H^{+}]$?

A student measures the mass of a copper block as $89.6 \pm 0.1$ g and its volume as $10.0 \pm 0.2$ $cm^{3}$. What is the density of the block reported with its absolute uncertainty?

When a graph of temperature ($T$) in $^{\circ}C$ is plotted against volume ($V$) for an ideal gas, where does the line intercept the x-axis?

Which of the following describes 'interpolation'?

If a graph of $y$ vs $x$ is a straight line through the origin with a gradient of $2$, what is the equation of the line?

What is the value of the gradient for a line that is parallel to the x-axis?

If a graph of $\ln([A]_t / [A]_0)$ against time ($t$) yields a straight line through the origin with a negative gradient, what is the order of the reaction?

A student measures the mass of a precipitate formed in a reaction. If they plot Mass (g) vs. Moles of limiting reactant (mol), what units will the gradient have?

In a graph of $1/[A]^2$ against time for a third-order reaction, the gradient represents which value?

A graph of the pressure of a real gas vs. its temperature ($T$ in Kelvin) at constant volume is linear but does not pass through the origin when extrapolated. This is due to the 'b' parameter in the Van der Waals equation, $(P + a/V^2)(V - b) = RT$. Which statement is true?

For a specific liquid, the relationship between surface tension ($\gamma$) and temperature ($T$) is $\gamma = \gamma_o(1 - bT)$. A plot of $\gamma$ vs $T$ has a gradient of $-0.15 \text{ mN m}^{-1} \text{ K}^{-1}$. If the surface tension at $0 \text{ K}$ is $72 \text{ mN m}^{-1}$, what is the value of the constant $b$?

A student performs a titration and plots $pH$ vs volume. They find the equivalence point is at $V = 25.0 \text{ cm}^3$. To find the uncertainty in this volume, they draw the steepest and shallowest possible sigmoid curves that fit within the error bars. The steepest curve crosses the inflection point at $24.8 \text{ cm}^3$ and the shallowest at $25.2 \text{ cm}^3$. What is the absolute uncertainty?

Which of the following radiation types has the shortest wavelength and thus the highest energy used in spectroscopic identification?

How many $^{1}$H NMR signals are observed for propane ($CH_{3}CH_{2}CH_{3}$)?

In IR spectroscopy, which bond corresponds to the range $1050-1410\text{ cm}^{-1}$?

A molecule has an IHD of 0. Which statement must be true?

Which molecule corresponds to an IR spectrum with a sharp peak at $1750\text{ cm}^{-1}$ and a mass spectrum with a base peak at $m/z = 43$?

In high-resolution $^{1}$H NMR, what is the multiplicity of the methyl signal in propanal ($CH_{3}CH_{2}CHO$)?

What is the IHD of the molecule naphthalene ($C_{10}H_{8}$)?

Calculate the IHD for a compound represented by the following skeletal structure: a bicyclic system (two fused six-membered rings) with one $C=C$ double bond and one $C=O$ group.

How many non-equivalent proton environments are in 2-methylbut-1-ene?

The IR spectrum of a compound shows a strong absorption at $1740\text{ cm}^{-1}$ and $1240\text{ cm}^{-1}$. The $^{1}$H NMR shows two singlets. Which compound is likely?