FE Chemical practice questions with answers

Answer: B) 5

For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc. Here that is 2·3 − 1·1 = 5.

• AIncorrect. This adds the two products (6 + 1). For a 2×2 matrix, the off-diagonal product is subtracted from the main-diagonal product.
• BCorrect. det = ad − bc = (2)(3) − (1)(1) = 6 − 1 = 5.
• CIncorrect. This is only the main-diagonal product (2 × 3). It leaves out the off-diagonal product, which must be subtracted.
• DIncorrect. This is only the off-diagonal product (1 × 1). The determinant is the main-diagonal product minus this term: 6 − 1.

Answer: A) Narrower

• ACorrect. The standard error shrinks with √n.
• BIncorrect. More data narrows the interval.
• CIncorrect. Width depends on n.
• DIncorrect. It narrows around the estimate.

Answer: C) 250 W

Power in a resistor is P = I²R = VI = V²/R. With I = 5 A and R = 10 Ω, P = 25 × 10 = 250 W.

• AIncorrect. 50 is the product I × R, which is the voltage across the resistor (50 V), not the power.
• BIncorrect. This applies a factor of ½ (½I²R), as if the 5 A were the peak of a sinusoidal AC current. For a steady DC current, P = I²R with no ½ factor.
• CCorrect. P = I²R = (5 A)² × 10 Ω = 250 W. As a check, V = IR = 50 V and P = VI = 50 × 5 = 250 W.
• DIncorrect. This uses I × R² = 5 × 100 = 500, which puts the square on the wrong variable. The correct expression is I²R.

Answer: A) High melting point and low thermal conductivity

• ACorrect. They contain heat and survive high temperature.
• BIncorrect. They're chosen for heat resistance.
• CIncorrect. Ceramics are brittle.
• DIncorrect. They're chosen for heat resistance.

Answer: C) 0.5 mol/kg

• AIncorrect. Divide by 2 kg.
• BIncorrect. That's inverted.
• CCorrect. Molality = moles solute per kg solvent.
• DIncorrect. Molality uses kg of solvent.

Answer: C) 45 kg/s

Mass flow rate is density times volumetric flow rate. The oil density is SG × 1,000 kg/m³ = 900 kg/m³, so ṁ = 900 × 0.05 = 45 kg/s.

• AIncorrect. This multiplies SG by Q but leaves out water's density of 1,000 kg/m³, so the oil density is never actually used.
• BIncorrect. This uses water's density (1,000 kg/m³) instead of the oil's density (900 kg/m³).
• CCorrect. ρ_oil = 0.9 × 1,000 = 900 kg/m³, so ṁ = ρQ = 900 × 0.05 = 45 kg/s.
• DIncorrect. This divides density by the flow rate (900/0.05) instead of multiplying them.

Answer: B) A two-phase mixture

• AIncorrect. Only part vaporizes.
• BCorrect. Enthalpy stays the same.
• CIncorrect. Pressure drops below saturation.
• DIncorrect. That isn't typical.

Answer: B) 20 wt%

• AIncorrect. Divide by the total mass.
• BCorrect. 20 ÷ (20 + 80).
• CIncorrect. That's water.
• DIncorrect. That isn't the calculation.

Answer: D) 1,129 kW

• AIncorrect. Recheck the decimal place.
• BIncorrect. Multiply by 0.5; don't divide.
• CIncorrect. Use the 0.5-kg/s rate.
• DCorrect. Q = ṁh_fg = 0.5(2,257).

Answer: A) the water-vapor partial pressure equals water's saturation pressure

The dew point is the temperature to which air must be cooled, at constant pressure and constant moisture content, to become saturated. At that point the vapor partial pressure equals the saturation pressure and condensation begins.

• ACorrect. Cooling at constant pressure and moisture content keeps the vapor partial pressure fixed. At the dew point that pressure equals the saturation pressure, so the air is saturated (100% RH) and condensation begins.
• BIncorrect. That describes boiling of pure water. The dew point of humid air is reached when the vapor partial pressure equals the saturation pressure at the air temperature.
• CIncorrect. Relative humidity rises as moist air cools at constant moisture content and reaches 100% at the dew point.
• DIncorrect. As air approaches saturation, the dry-bulb and wet-bulb temperatures converge. They are equal at saturation.

Answer: D) 75%

• AIncorrect. CSTRs can't reach full conversion.
• BIncorrect. That's one CSTR.
• CIncorrect. That's a PFR with kτ = 2.
• DCorrect. X = 1 − 1/(1 + kτ)² = 1 − 1/4.

Answer: B) $12,525

To convert a present investment into an equivalent annual cost, use the capital recovery factor: A = 50,000 × (A/P,8%,5) = 50,000 × 0.2505 ≈ $12,525.

• AIncorrect. This spreads $50,000 evenly over 5 years (50,000/5) and ignores interest. Recovering the capital at 8% costs more than this each year.
• BCorrect. A = P × (A/P,8%,5) = 50,000 × 0.2505 = $12,525 per year.
• CIncorrect. This adds 8% interest on the full $50,000 each year to the straight-line amount (10,000 + 4,000). It overstates the interest because the unrecovered balance drops each year. The capital recovery factor handles this correctly.
• DIncorrect. This uses the sinking fund factor (50,000 × 0.1705). That factor converts a future amount into an annual series. It doesn't apply to an amount invested today.

Answer: C) A closed discharge valve could raise pressure until something fails

• AIncorrect. That isn't the purpose.
• BIncorrect. It produces pressure on its own.
• CCorrect. The pump keeps delivering a fixed volume per stroke.
• DIncorrect. That isn't the reason.

Answer: C) Increases as the measured variable increases

• AIncorrect. That isn't control.
• BIncorrect. That's reverse acting.
• CCorrect. Reverse acting is the opposite.
• DIncorrect. It depends on the error.

Answer: D) Protect the vessel from overpressure

• AIncorrect. That's a gauge or transmitter.
• BIncorrect. That's a control valve.
• CIncorrect. That's a vacuum breaker.
• DCorrect. It opens at its set pressure.