FE Other Disciplines (NCEES Fundamentals of Engineering) — All Questions

What is the pH of a 0.001 M solution of the strong acid HCl?

• a.3✓
• b.2
• c.11
• d.1

HCl fully dissociates, so [H+] = 0.001 = 1x10^-3 M. pH = -log10[H+] = -log10(10^-3) = 3. A pH below 7 is acidic, consistent with an acid solution.

What is the oxidation state of sulfur in sulfuric acid, H2SO4?

• a.+2
• b.+4
• c.+6✓
• d.-2

Each H is +1 (total +2) and each O is -2 (total -8). For a neutral molecule the sum is zero: 2 + S + (-8) = 0, so S = +6. Assigning oxidation states this way underlies redox and corrosion analysis.

What is the molar mass of calcium carbonate, CaCO3? (Ca = 40, C = 12, O = 16 g/mol)

• a.100 g/mol✓
• b.72 g/mol
• c.116 g/mol
• d.60 g/mol

40 + 12 + 3(16) = 40 + 12 + 48 = 100 g/mol. Summing the atomic masses of every atom in the formula gives the molar (formula) mass.

How many moles are present in 36 g of water (H2O, molar mass 18 g/mol)?

• a.36 mol
• b.2 mol✓
• c.18 mol
• d.0.5 mol

moles = mass / molar mass = 36/18 = 2 mol. The mole links a measurable mass to a number of molecules through Avogadro's number.

What volume does 2 mol of an ideal gas occupy at standard temperature and pressure, where the molar volume is 22.4 L/mol?

• a.44.8 L✓
• b.24.0 L
• c.22.4 L
• d.11.2 L

V = n x 22.4 L/mol = 2 x 22.4 = 44.8 L. At STP one mole of any ideal gas occupies 22.4 L regardless of the gas's identity.

Using PV = nRT, what pressure is exerted by 1 mol of ideal gas in a 24.6 L vessel at 300 K? (R = 0.08206 L·atm/mol·K)

• a.1.0 atm✓
• b.2.0 atm
• c.0.5 atm
• d.24.6 atm

P = nRT/V = (1)(0.08206)(300)/24.6 = 24.6/24.6 = 1.0 atm. The ideal gas law ties P, V, n, and T together through the universal gas constant R.

What is the molarity of a solution containing 0.5 mol of NaCl dissolved in enough water to make 2 L of solution?

• a.0.5 M
• b.2.0 M
• c.0.25 M✓
• d.1.0 M

Molarity = moles of solute / liters of solution = 0.5/2 = 0.25 M. Molarity is defined per liter of total solution, not per liter of solvent.

To what volume must 100 mL of 6.0 M HCl be diluted to obtain a 1.0 M solution? (M1V1 = M2V2)

• a.166 mL
• b.300 mL
• c.60 mL
• d.600 mL✓

V2 = M1V1/M2 = (6.0)(100)/(1.0) = 600 mL. Dilution conserves the moles of solute, so concentration and volume vary inversely.

What is the pH of a 0.01 M solution of the strong base NaOH at 25 degC?

• a.2
• b.7
• c.12✓
• d.10

NaOH dissociates fully, so [OH-] = 0.01, pOH = -log(0.01) = 2, and pH = 14 - pOH = 12. Strong bases give a pH well above 7.

What is the pH of a 1 x 10^-4 M solution of the strong acid HCl?

• a.10
• b.4✓
• c.3
• d.2

HCl dissociates fully, so [H+] = 1 x 10^-4 M and pH = -log(10^-4) = 4. Each tenfold dilution of a strong acid raises the pH by one unit.

In the reaction 2 H2 + O2 -> 2 H2O, how many grams of water form from 2 mol of H2 with excess O2? (H2O = 18 g/mol)

• a.9 g
• b.36 g✓
• c.18 g
• d.72 g

The 2:2 mole ratio gives 2 mol H2 -> 2 mol H2O; mass = 2 x 18 = 36 g. Balanced-equation coefficients set the mole ratios of reactants to products.

For N2 + 3 H2 -> 2 NH3, if 1 mol N2 reacts with 2 mol H2, which is the limiting reactant?

• a.N2
• b.Neither; they are stoichiometric
• c.H2✓
• d.NH3

The reaction needs 3 mol H2 per mol N2, but only 2 mol H2 is available, so hydrogen runs out first and limits the product. Nitrogen is in excess.

What is the mass percent of oxygen in water, H2O? (H = 1, O = 16 g/mol)

• a.88.9%✓
• b.16%
• c.11.1%
• d.50%

Oxygen contributes 16 of the total 18 g/mol, so 16/18 = 88.9%. Mass percent weights each element by its atomic mass, not by atom count.

Approximately how many molecules are in 2 mol of a substance? (Avogadro's number = 6.02 x 10^23 /mol)

• a.3.01 x 10^23
• b.1.20 x 10^23
• c.1.20 x 10^24✓
• d.6.02 x 10^23

Number = n x N_A = 2 x 6.02 x 10^23 = 1.20 x 10^24 molecules. Avogadro's number defines how many entities make up one mole.

What is the oxidation state of manganese in the permanganate ion, MnO4^-? (O = -2)

• a.+2
• b.+7✓
• c.+5
• d.+4

Four oxygens contribute -8; the overall ion charge is -1, so Mn + (-8) = -1, giving Mn = +7. Permanganate is a strong oxidizer because Mn is at its highest state.

When methane burns completely as CH4 + a O2 -> CO2 + b H2O, what are the coefficients a and b?

• a.a = 1, b = 2
• b.a = 2, b = 2✓
• c.a = 2, b = 1
• d.a = 1, b = 1

Balancing carbon gives 1 CO2, hydrogen gives 2 H2O, and oxygen then needs 2 O2: CH4 + 2 O2 -> CO2 + 2 H2O. Every element's atoms must balance.

A first-order reaction has a rate constant k = 0.693 min^-1. What is its half-life? (t-half = 0.693/k)

• a.0.693 min
• b.2.0 min
• c.1.0 min✓
• d.0.5 min

t-half = 0.693/k = 0.693/0.693 = 1.0 min. For first-order kinetics the half-life is constant and independent of the initial concentration.

For the exothermic equilibrium N2 + 3 H2 <=> 2 NH3, increasing the temperature will:

• a.Have no effect on the equilibrium
• b.Shift the equilibrium toward more NH3
• c.Shift the equilibrium toward the reactants (less NH3)✓
• d.Stop the reaction entirely

By Le Chatelier's principle, adding heat to an exothermic reaction favors the endothermic (reverse) direction, decreasing the NH3 yield.

What is the normality of a 2 M sulfuric acid (H2SO4) solution acting as a diprotic acid?

• a.4 N✓
• b.2 N
• c.1 N
• d.0.5 N

Normality = molarity x equivalents per mole. H2SO4 supplies 2 H+ per molecule, so N = 2 x 2 = 4 N. Normality counts reactive equivalents, not just moles.

A water sample contains 5 mg of dissolved solids per liter. Expressed in ppm (mg/L in dilute water), this is:

• a.50 ppm
• b.5 ppm✓
• c.0.5 ppm
• d.500 ppm

In dilute aqueous solution 1 mg/L is about 1 ppm because 1 L of water has a mass near 1 kg (10^6 mg). So 5 mg/L = 5 ppm.

At a fixed temperature and pressure, the density of an ideal gas is directly proportional to its:

• a.Color
• b.Specific heat
• c.Volume
• d.Molar mass✓

From PV = nRT with n = m/M, density rho = PM/(RT). At fixed T and P, density is proportional to molar mass M, so heavier molecules give denser gases.

A reaction releases heat to its surroundings. Its enthalpy change (delta H) is therefore:

• a.Negative (exothermic)✓
• b.Positive (endothermic)
• c.Always equal to the activation energy
• d.Zero

Exothermic reactions release energy, so the products have lower enthalpy than the reactants and delta H < 0. Endothermic reactions absorb heat with delta H > 0.

A compound is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass (C = 12, H = 1, O = 16). What is its empirical formula?

• a.C2H6O
• b.CH2O✓
• c.C2H4O2
• d.CHO

Moles: C 40/12 = 3.33, H 6.7/1 = 6.7, O 53.3/16 = 3.33. Dividing by 3.33 gives 1:2:1, so CH2O. The empirical formula uses the smallest whole-number atom ratio.

In electrolysis, the mass of metal deposited at the cathode is, by Faraday's laws, proportional to:

• a.The total electric charge (current x time) passed✓
• b.The color of the electrode
• c.The applied voltage only
• d.The temperature of the bath

Faraday's first law states that deposited mass is proportional to the charge Q = I*t passed, scaled by the equivalent weight. Doubling current or time doubles the deposit.