Ratios problem solving using

There have been several theories proposed to explain the anomalous 3/4 power-law dependence of the contact radius on particle radius in what should be simple JKR systems. Maugis [60], proposed that the problem with using the JKR model, per se, is that the JKR model assumes small deformations in order to approximate the shape of the contact as a parabola. In his model, Maugis re-solved the JKR problem using the exact shape of the contact. According to his calculations, o should vary as / , where 2/3 < y < 1, depending on the ratio a/R. 

Regardless of which form is used, the meaning is the same There were 25 women for every 16 men. Notice that is a fractional form of a ratio. The fractional form of a ratio is often a convenient way to represent a ratio when solving problems. 

Equation (8.47), with t = 0 and the composition of lead from meteoritic troilite used for the initial isotopic ratio of lead, was used by Clair Patterson (1955,1956) to determine the age of the Earth. In the 1950s, the largest uncertainty in determining the age of the Earth was the composition of primordial lead. In 1953, Patterson solved this problem by using state-of-the-art analytical techniques to measure the composition of lead from troilite (FeS) in iron meteorites. Troilite has an extremely low U/Pb ratio because uranium was separated from the lead in troilite at near the time of solar-system formation. Patterson (1955) then measured the composition of lead from stony meteorites. In 1956, he demonstrated that the data from stony meteorites, iron meteorites, and terrestrial oceanic sediments all fell on the same isochron (Fig. 8.20). He interpreted the isochron age (4.55+0.07 Ga) as the age of the Earth and of the meteorites. The value for the age of the Earth has remained essentially unchanged since Patterson s determination, although the age of the solar system has been pushed back by —20 Myr. 

Ratio problems may ask you to determine the number of items in a group based on a ratio. You can use the concept of multiples to solve these problems. 

You can use proportions to solve ratio problems that ask you to determine how much of something is needed based on how much you have of something else. 

General buckling in a slender column with a slenderness ratio, L/D, greater than 100, occurs when it is subjected to a critical compressive load. This load is much lower than the maximum load allowable for compressive yield. Although this problem can be easily solved using Euler s equation1, which predicts the critical load applied to the slender column, it lends itself very well to illustrate dimensional analysis. 

The work by Osswald et.al [12] was done to understand this phenomenon. To simulate the effect shown in the photograph, they used the two-dimensional mesh and processing conditions presented in Fig. 9.23. Note that in order to better see the set-up and results, the mesh is shown distorted in the thickness direction of the charge. Since the thickness-to-length (L/D) ratio is very small, the heat transfer in the non-isothermal solution reduces to a ID problem, and was solved using the finite difference technique. 

We can use ratios to solve problems. Pairs of equivalent ratios, or fractions, are called proportions. 

In this problem, there are 3 outer loop decision variables, N and the recovery of component 1 from each mixture (Re1 D1B0, Re D2,BO)- Two time intervals for reflux ratio were used for each distillation task giving 4 optimisation variables in each inner loop optimisation making a total of 8 inner loop optimisation variables. A series of problems was solved using different allocation time to each mixture, to show that the optimal design and operation are indeed affected by such allocation. A simple dynamic model (Type III) was used based on constant relative volatilities but incorporating detailed plate-to-plate calculations (Mujtaba and Macchietto, 1993 Mujtaba, 1997). The input data are given in Table 7.3. 

Stoichiometry problems involving reactions can always be solved using mole ratios. 

Stoichiometry problems can be solved using three basic steps. First, change what you are given into moles. Second, use a mole ratio based on a balanced chemical equation. Third, change to the units needed for the answer. 

Why is it necessary to use mole ratios in solving stoichiometry problems ... 

To solve the problem, you need to know how the unknown moles of hydrogen are related to the known moles of potassium. In Section 12.1 you learned to use the balanced chemical equation to write mole ratios that describe mole relationships. Mole ratios are used as conversion factors to convert a known number of moles of one substance to moles of another substance in the same chemical reaction. What mole ratio could be used to convert moles of potassium to moles of hydrogen In the correct mole ratio, the moles of unknown (H2) should be the numerator and the moles of known (K) should be the denominator. The correct mole ratio is... 

Note, although Furlonge et al. (1999) reported that variable hold-ups in the vessels of MultiVBD reduces energy consumption, in this work, we distributed the feed in different vessels according to the product profiles calculated a priori. Also, for conventional column piecewise constant reflux ratio with two intervals were used for each cut. The above optimisation problem is solved using gPROMS software. Note, for CBD column, two reflux intervals were considered for each cut and the reflux ratio in each interval was assumed to be piecewise constant (Mujtaba, 2004). 

We have set up the dimensional equation with vertical lines to separate each ratio, and these lines retain the same meaning as an X or multiplication sign placed between each ratio. The dimensional equation will be retained in this form throughout most of this text to enable you to keep clearly in mind the significance of units in problem solving. It is recommended that you always write down the units next to the associated numerical value (unless the calculation is very simple) until you become quite familiar with the use of units and dimensions and can carry them in your head. 

Mole-mole problems are sort of like introductory, or skill-building, problems that will help you practice using the molar ratios given by balanced chemical reactions. The harder stoichiometry problems, which we will begin in the next lesson, all make use of mole-mole problems as a step in the problem-solving process. This lesson will give you an opportunity to become comfortable with the molar ratio without worrying about more complex problems at the same time. 

Problem-Solving Tip Use the Mole Ratio in Calculations with... 

To convert masses to moles or vice versa, we use the molar mass of the substance. Molar mass has the same numeric value as the number of atomic mass units in a formula unit, but it is expressed in units of grams per mole. For example, the molar mass of water is 18.0 g/mol because the formula mass of water is 18.0 amu/molecule. Because molar mass is a ratio, it can be used as a factor in problem solving. 

To solve for Ck, the generalized eigenvalue problem is used with the singular-value decomposition technique. The results of the problem indicate both the pure component response patterns x and y and the ratio of concentrations of the pure components to the standard response concentration. 

Additionally, in Laue geometry only cell ratios can be determined from the angular coordinates of spots. The absolute cell parameters therefore have to be provided from a monochromatic study. However, if the intensities of spots are also considered, then there appears to be scope to solve the problem by using knowledge of Amin (section 7.2.3) and the bromine K edge in the photographic film as wavelength markers. 

In Chapters 3 and 4, we encountered many reactions that involved gases as reactants (e.g., combustion with O2) or as products (e.g., a metal displacing H2 from acid). From the balanced equation, we used stoichiometrically equivalent molar ratios to calculate the amounts (moles) of reactants and products and converted these quantities into masses, numbers of molecules, or solution volumes (see Figure 3.10). Figure 5.11 shows how you can expand your problem-solving repertoire by using the ideal gas law to convert between gas variables (F, T, and V) and amounts (moles) of gaseous reactants and products. In effect, you combine a gas law problem with a stoichiometry problem it is more realistic to measure the volume, pressure, and temperature of a gas than its mass. 

Delaney JS, Dyar MD, Sutton SR, Bajt S (1998) Redox ratios with relevant resolution Solving an old problem by using the synchrotron microXANES probe. Geology 26 139-142 Delaney JS, Jones JH, Sutton SR, Simon S, Grossman L (1999) In situ microanalysis of vanadium, chromium, and iron oxidation states in extraterrestrial samples by synchrotron microXANES (SmX) spectroscopy. Meteorit Planet Sci 34 A32... 

We could solve this problem by using the ideal gas equation, but we can take a shortcut by using the molar volume of an ideal gas at STP. Since 1 mole of an ideal gas at STP has a volume of 22.42 L, 1.75 L N2 at STP will contain less than 1 mole. We can find how many moles using the ratio of 1.75 L to 22.42 L ... 

---