Nutrition is a common topic in the media, whether it’s a new diet plan or a new “superfood” on the market to benefit our health. Some of these products are scientifically sound, while others aren’t. How do we tell the difference?

The first-order reaction a→2b+c has rate constant 0.538 s−1. if the initial concentration of a is 0.867 mol l−1, what is the half-life of the reaction in seconds? remember to use correct significant figures in your answer (round your answer to the nearest hundredth). do not include units in your response.

8.29 two streams containing pyridine and acetic acid at 25°c are mixed and fed into a heat exchanger. due to the heat-of-mixing effect, it is desired to reduce the temperature after mixing to 25°c using a stream of chilled ethylene glycol as indicated in the diagram. calculate the mass flow rate of ethylene glycol needed. the heat capacity of ethylene glycol at these conditions is approximately 2.8 kj/(kg k), and the enthalpy change of mixing (δmixh) is given below.

Find an expression for the electric field e⃗ at the center of the semicircle. hint: a small piece of arc length δs spans a small angle δθ=δs /r, where r is the radius. express your answer in terms of the variables q, l, unit vectors i^, j^, and appropriate constants.