Free FE Chemical Practice Questions

Sample Practice Questions

Try these 10 sample questions from the FE Chemical practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1An acute angle in a right triangle has an opposite side of 6 cm and a hypotenuse of 10 cm. What is the angle, to the nearest 0.1°?

   1. A. 30.0°
   2. B. 36.9°
   3. C. 53.1°
   4. D. 60.0°

   Answer: B

   Explanation: The handbook states, "The inverse trigonometric function, also known as the arc function, defines the angle based on the value of the trigonometric function." Here sin θ = 6/10, so θ = arcsin(0.6) = 36.9°. Using the complementary ratio gives 53.1°; 30° and 60° use standard-angle values that do not match this ratio.

   Reference: DOE Fundamentals Handbook: Mathematics, Volume 2 — Module 4, pp. 4–7, Trigonometric Functions and Inverse Trigonometric Functions

2. 2A 10 kg cart experiences a 50 N horizontal force to the right and a 20 N horizontal resistance to the left. What is its horizontal acceleration?

   1. A. 2.0 m/s² to the right
   2. B. 3.0 m/s² to the right
   3. C. 5.0 m/s² to the right
   4. D. 7.0 m/s² to the right

   Answer: B

   Explanation: The handbook states, "the acceleration of a body is proportional to the net (i.e., sum or resultant) force acting on it and in the direction of that net force." Equation 3-1 gives F = ma. The net force is 50 − 20 = 30 N, so a = 30/10 = 3.0 m/s² rightward. The alternatives use the resistance alone, the applied force alone, or add opposing forces.

   Reference: DOE Fundamentals Handbook: Classical Physics — Module 3, p. 1, Newton’s Laws of Motion, equation 3-1

3. 3A solution contains 0.25 mol of NaCl in a final solution volume of 500 mL. What is its molarity?

   1. A. 0.125 mol/L
   2. B. 0.250 mol/L
   3. C. 0.500 mol/L
   4. D. 2.000 mol/L

   Answer: C

   Explanation: The handbook states, "Molarity is defined as moles of solute per liter of solution." Therefore M = 0.25/0.500 = 0.500 mol/L. Multiplying instead of dividing gives 0.125; ignoring the volume gives 0.250; inverting the ratio gives 2.000.

   Reference: DOE Fundamentals Handbook: Chemistry, Volume 1 — Module 1, p. 37, Molarity

4. 4Which fluid property measures resistance to deformation under a shear force?

   1. A. Density
   2. B. Viscosity
   3. C. Compressibility
   4. D. Specific volume

   Answer: B

   Explanation: DOE states, "Viscosity is a fluid property that measures the resistance of the fluid to deforming due to a shear force." Density is mass per volume, compressibility concerns pressure-induced volume change, and specific volume is volume per mass.

   Reference: DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Volume 3 — Module 3, p. 19, Viscosity

5. 5A steady mixer combines 30 kg/h of a 10 wt% salt solution with 70 kg/h of a 30 wt% salt solution. With no reaction or separation, what is the outlet salt mass fraction?

   1. A. 0.18
   2. B. 0.20
   3. C. 0.24
   4. D. 0.40

   Answer: C

   Explanation: DOE states that "all mass flow rates into a control volume are equal to all mass flow rates out of the control volume plus the rate of change of mass within the control volume." Applying steady balances to total mass and nonreacting salt gives 100 kg/h total and 30(0.10) + 70(0.30) = 24 kg/h salt. The mass fraction is 24/100 = 0.24. Equal-weight averaging gives 0.20 and adding feed fractions gives 0.40; neither uses the component flow balance.

   Reference: DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Volume 3 — Module 3, p. 10, Conservation of Mass

6. 6A dilute species has constant molecular diffusivity 2.0 × 10^−9 m²/s and a concentration-gradient magnitude of 50 mol/m⁴. Using Fick's first law, what is the magnitude of its diffusive molar flux?

   1. A. 1.0 × 10^−7 mol/(m²·s)
   2. B. 4.0 × 10^−11 mol/(m²·s)
   3. C. 2.5 × 10^10 mol/(m²·s)
   4. D. 1.0 × 10^−9 mol/(m²·s)

   Answer: A

   Explanation: COMSOL describes diffusive molar flux as "proportional to the concentration gradient." Its magnitude is D|∇C| = (2.0 × 10^−9)(50) = 1.0 × 10^−7 mol/(m²·s). The other choices divide instead of multiply or misapply powers of ten.

   Reference: COMSOL: Diffusion Equation—Fick’s Laws — Fick’s Laws and Fick’s First Law of Diffusion

7. 7A hydrolysis reaction is first order in dissolved reactant. At unchanged temperature and solution conditions, how does doubling its concentration affect the volumetric reaction rate?

   1. A. The rate stays unchanged.
   2. B. The rate doubles.
   3. C. The rate increases fourfold.
   4. D. The rate decreases by half.

   Answer: B

   Explanation: EPA states, "Hydrolysis rate is first order with respect to constituent concentrations." With r = kC and k unchanged, doubling C doubles r. Unchanged rate implies zero order, a fourfold increase implies second order, and a halved rate implies inverse dependence.

   Reference: EPA Industrial Waste Air Model Technical Background Document — Section 2.4.4, Surface Impoundments, page 2-36

8. 8At an effective annual discount rate of 10%, what is the present worth of $1,210 received at the end of year 2?

   1. A. $1,000
   2. B. $1,100
   3. C. $1,210
   4. D. $1,464.10

   Answer: A

   Explanation: NIST explains that the SPV factor calculates the present value "of a future cash amount (Ft) occurring at the end of year t given discount rate d." Thus P = 1210/(1.10)² = $1000. The distractors discount once, omit discounting, or compound forward instead.

   Reference: NIST Handbook 135: Life Cycle Costing Manual for the Federal Energy Management Program — Chapter 3, Figure 3-1, Single present value formula, page 23

9. 9A stable linear process has G(s) = 3/(5s + 1). For a sustained input step of 2 units from an initial steady state, what is the eventual change in output?

   1. A. 0.4 unit
   2. B. 1.2 units
   3. C. 6 units
   4. D. 10 units

   Answer: C

   Explanation: The documented first-order model is "Kp G(s) = ---------- 1+Tp1*s". Its steady-state gain is Kp = 3, so the output change is 3 × 2 = 6 units. The alternatives divide by the time constant, divide the gain response by it, or multiply input by it.

   Reference: MathWorks Building and Estimating Process Models Using System Identification Toolbox — Representation of Process Models Using IDPROC Objects, P1 transfer function

10. 10Under the NSPE Code, an engineer lacking education or experience in a specialized technical field is asked to personally approve its design documents. Which response meets the competence obligation?

    1. A. Sign because the employer accepts the schedule risk.
    2. B. Sign after adding a disclaimer of technical responsibility.
    3. C. Have the qualified engineer responsible for that technical work approve it.
    4. D. Sign if the client agrees to pay for later corrections.

    Answer: C

    Explanation: The NSPE Code limits services to "areas of their competence". Personal approval cannot be justified by schedule pressure, a disclaimer, or willingness to fund corrections. Responsibility for the specialized technical segment belongs with an appropriately qualified engineer; overall coordination does not waive that requirement.

    Reference: NSPE Code of Ethics for Engineers — I.2 and II.2, competence and technical segments