Methane at $25^{\circ} \mathrm{C}$ is burned in a boiler furnace with 10.0% excess air preheated to $100^{\circ} \mathrm{C}$. Ninety percent of the methane fed is consumed, the product gas contains $10.0 \mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO}$, and the combustion products leave the furnace at $400^{\circ} \mathrm{C}$. a) Calculate the heat transferred from the furnace, -Q(kW), for a basis of 100 mol $\mathrm{CH}_{4}$ fed/s. (The greater the value of -Q, the more steam is produced in the boiler.) b) Would the following changes increase or decrease the rate of steam production? (Assume the fuel feed rate and fractional conversion of methane remain constant.) Briefly explain your answers. (i) Increasing the temperature of the inlet air; (ii) increasing the percent excess air for a given stack gas temperature; (iii) increasing the selectivity of $\mathrm{CO}_{2}$ formation in the furnace; and (iv) increasing the stack gas temperature.

Discuss the following problem. According to Newton’s laws of motion, an ion exposed to an electric field in a vacuum would experience a constant acceleration from the electric driving force, just as a falling body in a vacuum constantly accelerates due to gravity. In water, however, an ion moves at constant velocity in an electric field. Why do you suppose that is?

A 0.1 mole% caustic soda (NaOH) solution is to be concentrated in a continuous evaporator. The solution enters the unit at $25^{\circ} \mathrm{C}$ at a rate of 150 mol/min and is concentrated to 5 mole% at $60^{\circ} \mathrm{C}$. Hot dry air at $200^{\circ} \mathrm{C}$ and 1.1 bar absolute is bubbled through the evaporator and leaves saturated with water at $60^{\circ} \mathrm{C}$ and 1 atm. Calculate the required volumetric flow rate of the entering air and the rate at which heat must be transferred to or from the unit. Assume that the heat capacity per unit mass of all liquid solutions is that of pure water.

A stream of pure cyclopentane vapor flowing at a rate of $1550 \mathrm{L} / \mathrm{s} \text { at } 150^{\circ} \mathrm{C}$ and 1 atm enters a cooler in which 65% of the feed is condensed at constant pressure. a) What is the temperature at the condenser outlet? Explain how you know (a single sentence should suffice). b) Prepare and fill in an inlet–outlet enthalpy table and calculate the required cooling rate in kW.

A fuel gas containing 95 mole% methane and the balance ethane is burned completely with 25% excess air. The stack gas leaves the furnace at $900^{\circ} \mathrm{C}$ and is cooled to $450^{\circ} \mathrm{C}$ in a waste-heat boiler, a heat exchanger in which heat lost by cooling gases is used to produce steam from liquid water for heating, power generation, or process applications. a) Taking as a basis of calculation 100 mol of the fuel gas fed to the furnace, calculate the amount of heat (kJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling. b) How much saturated steam at 50 bar can be produced from boiler feedwater at $40^{\circ} \mathrm{C}$ for the same basis of calculation? (Assume all the heat transferred from the gas goes into the steam production.) c) At what rate (kmol/s) must fuel gas be burned to produce 1280 kg steam per hour (an amount required elsewhere in the plant) in the waste heat boiler? What is the volumetric flow rate $\left(\mathrm{m}^{3} / \mathrm{s}\right)$ of the gas leaving the boiler? d) Briefly explain how the waste-heat boiler contributes to the plant profitability. (Think about what would be required in its absence.)

Discuss the following problem. Virtually all cancer treatments are designed to kill cancer cells, usually by inducing apoptosis. However, one particular cancer-acute promyelocytic leukemia (APL)-has been successfully treated with all-trans-retinoic acid, which causes the promyelocytes to differentiate into neutrophils. How might a change in the state of differentiation of APL cancer cells help the patient?

If $x_{ij} = i + j^2$, determine (a) $\sum_{j=1}^{3} \sum_{i=1}^{2} x_{i j}$ (b) $\sum_{i=1}^{2} \sum_{j=1}^{3} x_{i j}$

Given the initial-value problem, use the three-term Taylor formula to obtain a four-decimal approximation to the indicated value. First use (a) h=0.1 and then (b) h=0.05. $y^{\prime}=y-y^{2}, y(0)=0.5; y(0.5)$

A sample of size 120 had a sample mean of 100 and a sample standard deviation of 15. Of these 120 data values, 3 were less than 70; 18 were between 70 and 85; 30 were between 85 and 100; 35 were between 100 and 115; 32 were between 115 and 130; and 2 were greater than 130. Test the hypothesis that the sample distribution was normal.

A steam turbine, operating reversibly and adiabatically, takes in superheated steam at 2000 kPa and discharges at 50 kPa. (a) What is the minimum superheat required so that the exhaust contains no moisture? (b) What is the power output of the turbine if it operates under these conditions and the steam rate is $5 kg \cdot s^{-1}?$

Calculate the amount of heat (in kJ) required to raise the temperature of a 79.0 g sample of ethanol from 298.0 K to 385.0 K.

The efficiency of an engine is 0.21. For every 1.00 kJ of beat absorbed by the engine, how much (a) net work is done by it and (b) heat is released by it?

The heat capacity at a constant pressure of a certain amount of a diatomic gas is $14.4 \text{~J/K}$. $(d)$ What is the heat capacity of this gas at constant volume?

The azide ion, $N_3 ^-$, is a symmetrical ion, all of whose contributing resonance structures have formal charges. Draw three important contributing structures for this ion.