List of top Questions asked in GATE CH

Consider the following homogeneous isothermal liquid-phase parallel reactions carried out in three reactor configurations (having identical volumes and same operating temperatures), as shown in the figure.
\[ A + B \rightarrow D \qquad \text{Rate of formation of D: } r_D = k_1 C_A C_B \]\[ A + B \rightarrow U \qquad \text{Rate of formation of U: } r_U = k_2 C_A^2 C_B \]
where D is the desired product and U is the undesired product. The inlet concentrations of A and B are the same in all three configurations (\(C_{A0}=C_{B0}=1\ \text{mol L}^{-1}\)). The total molar feed flow rate of A (\(F_{A0}\)) and that of B (\(F_{B0}\)) are the same in all three configurations (\(F_{A0}=F_{B0}=10\ \text{mol min}^{-1}\)). In configuration I, \(F_{A0}\) is equally distributed among all the inlets. Similarly, in configuration III, \(F_{B0}\) is equally distributed among all the inlets. Assuming plug flow behavior, at steady state, which one of the following statements is CORRECT?

Vapor pressure of water at various temperature is given in the table.

Temperature (in K)	284	289	294	299	310
Vapor pressure of water (in kPa)	1.28	1.80	2.50	3.40	6.40

Consider a flow with the following velocity field
\[ \vec{V} = (x+y)\hat{i} + (y+z)\hat{j} + (z+x)\hat{k} \]
where \(\hat{i}\), \(\hat{j}\) and \(\hat{k}\) are the unit vectors in the x, y and z directions, respectively. Which one of the following is CORRECT?

K value is defined as the ratio of mole fraction of a component in the vapor phase to that in the liquid phase. The K values of propane and iso-butane at 293 K are given in the table.

Pressure (kPa)	K value: Propane	K value: iso-Butane
1100	1.8	0.85
1200	1.6	0.75
1300	1.4	0.65
1400	1.25	0.5
1500	1.1	0.45

Which one of the following is closest to the bubble point pressure (in kPa) of an equimolar mixture of propane and iso-butane at 293 K?

Using single step trapezoidal rule, the value of
\[ \int_{0}^{0.5} (1+16x-20x^2)\,dx \]
is ______ (rounded off to two decimal places).

A volatile organic compound (VOC) is to be adsorbed from air onto a bed of activated carbon. The equilibrium capacity of activated carbon at the feed conditions is 0.4 grams VOC per gram of activated carbon. The column contains 4 grams of activated carbon per cm² of cross-section. The feed rate into the adsorber column is 0.2 grams VOC cm^-2 h^-1. Breakthrough time is defined as the time at which the concentration at the exit of the bed (c) reaches a value of \(0.05c_0\), where \(c_0\) is the concentration of VOC in the feed. The breakthrough time for the bed is 2.1 h. The area under \(c/c_0\) curve between the initial and breakthrough times is 0.1 h. Which one of the following is the fraction of unused bed at breakthrough?

An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:
Event A: The outcome of the rolled die is a prime number.
Event B: The outcome of the rolled die is an odd number less than 4.
The conditional probability of A given B, denoted by P(A|B), is ______ (rounded off to one decimal place).

Consider a non-reactive binary mixture of two ideal gases A and B in an isothermal horizontal closed tube. Due to the concentration difference at the two ends of the tube, equimolal counterdiffusion occurs along the axial direction. No concentration gradients exist in the radial direction. The profile for partial pressure of component A (\(p_A\)) as a function of axial distance \(z\) is shown in the figure. The partial pressure of component B (\(p_B\)) approaches zero at \(z = 0.8\) m. At a location \(z = z_1\) the partial pressures of the components A and B are equal. The value of \(z_1\) (in m) is ______ (rounded off to two decimal places).

Water is discharged from the vertical side of a tank through a circular orifice of diameter 2 cm under laminar flow conditions. The water surface in the tank is maintained at a constant level above the center of the orifice. If the fluid jet has a diameter of 1.6 cm at its vena contracta, then the coefficient of contraction is ______ (rounded off to two decimal places).

Consider a homogeneous gas phase reaction, \(A + 2B \rightarrow 2C + 3D\), occurring at constant temperature and pressure in a varying volume batch reactor. The vessel is initially charged with 50 moles of A and 150 moles of B. The gases behave ideally. For complete conversion of A, the ratio of the final volume to the initial volume is ______ (rounded off to one decimal place).

In which of the following condition(s), Bernoulli's equation is applicable?

Which of the following methods for calculating profitability does/do NOT consider the time value of money?

Consider two successive screen sizes in the Tyler standard screen scale, viz. 150 meshes per inch and 200 meshes per inch. Their linear sizes of the openings are L150 and L200, respectively. If the value of L200 is \(2.9 \times 10^{-3}\) inch, then the value of L150 (in inch) is \(\times 10^{-3}\) (rounded off to one decimal place).

Which of the following statements regarding the heat of reaction is/are CORRECT?

Which one of the following is produced by catalytic reforming of straight run gasoline and naphtha?

Urea has its major use as a solid fertilizer for nitrogen fixation. Which of the following is/are other application(s) of urea?

A process exhibits an inverse response to a step input. Which of the following statements is/are necessarily TRUE about the process?

Which one of the following is the pair of eigenvalues of the matrix \( \begin{bmatrix} -3 & 4 \\ 4 & 3 \end{bmatrix} \)?

Which one of the following is the value of \( \displaystyle\lim_{x \to 0} \frac{e^{x} - x - 1}{\cos x - 1} \)?

An irreversible chemical reaction occurs on a porous catalyst. All the pores are of same size. In strong pore diffusion regime, the observed activation energy is 120 kJ mol^-1. The activation energy of diffusion is 10 kJ mol^-1. Assuming Arrhenius temperature dependency for both reaction and diffusion, which one of the following is the true activation energy (in kJ mol^-1) of the reaction?

For an irreversible reaction containing inerts in the feed, the single-pass conversion in a reactor is 70%. Which one of the following statements is CORRECT?

A two-dimensional temperature profile is given as \( T = 2x^2 + 3xy + y^2 \). If \(\hat{\imath}\) and \(\hat{\jmath}\) are the unit vectors along x and y directions, respectively, which one of the following is the directional derivative of T at the location x = 2, y = 2?

In a traditional continuous Kraft (Sulfate) pulping process, consider the following major steps:
Bleaching (BL), Chipping (CH), Debarking (DE), Digestion (DI), and Pulp Washing (WA).
Which one of the following is the CORRECT sequence of steps for this process?

A binary mixture of butane and butadiene is to be separated in an extractive distillation using furfural. Furfural lowers the activity of butadiene more than it does for butane. Consider the distillation sequence shown in the figure.

Match the component labels in Group I with the chemical species in Group II.

Group I	Group II
P. Component X	1. Butane
Q. Component Y	2. Butadiene
R. Component Z	3. Furfural

According to the phase rule, which one of the following is the number of degrees of freedom for pure water at its triple point?