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Math Help - Converting questions, and how to find isotopes protons neutrons.

  1. #1
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    Converting questions, and how to find isotopes protons neutrons.

    I have a few questions i need some help on. its converting (my weakest category).

    1)What is the price of 1 gallon of gasoline in U.S. dollars in France? (The value of the Euro is currently $1.33 U.S. and the price of 1 liter of gasoline in France is 0.90 Euro.)

    2)What is its density in pounds per cubic inch (lb/inch^3).
    (The density of lead is 11.4 .)
    3)How many kilometers can the Insight travel on the amount of gasoline that would fit in a soda pop can? The volume of a soda pop can is 355 .
    (The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of 57 in the city.)

    and last how do i solve for protons and neutrons if something says

    , ,, etc? thxs for teh help.
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  2. #2
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    If you are just starting out, it pays to do things one step at a time. For now, it takes a bit longer but makes it really clear. With practice you should be able to skip quite a few steps.

    1)What is the price of 1 gallon of gasoline in U.S. dollars in France? (The value of the Euro is currently $1.33 U.S. and the price of 1 liter of gasoline in France is 0.90 Euro.)
    Let x = the price of a gallon of gas in USD. I will refer to gallon as G in the following equation.

    First off we have  \frac{0.9 \,Euro}{1 L}

    1 euro = 1.33 USD
     0.9 \,Euro = 1 \times \frac{9}{10} \, Euro = 1.33 \times \frac{9}{10} \,  USD = 1.197 \, USD

    So now we have  \frac{0.9 \,Euro}{1 L} = \frac{1.197 \, USD }{1 L}

    1 Litre = 0.264 liquid Gallons (US) so we have

    \frac{0.9 \,Euro}{1 L}  = \frac{1.197 \, USD }{1 L} = \frac{1.197 \, USD}{0.264 G} = \frac{4.534 \, USD }{1G}

    2)What is its density in pounds per cubic inch (lb/inch^3).
    (The density of lead is 11.4 .)
    Please try to work this out yourself using question 1 as a guide. 1g = 453.6 lbs and 1 inch = 2.54 cm. Ask for more help and show your working so far if you really can't do it.

    3)How many kilometers can the Insight travel on the amount of gasoline that would fit in a soda pop can? The volume of a soda pop can is 355 .
    (The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of 57 in the city.)
    Same as question 2. 1 mile = 1.61 km

    and last how do i solve for protons and neutrons if something says

    , ,, etc?
    You'll need a periodic table for this. Most periodic tables have two numbers - one is an integer, which ascends consecutively from left to right, continuing on the next row. The other one is a larger number with decimal places.

    The integer is called the atomic number. It is defined as the number of protons in the element. In a non-ionised state, each element has the same number of protons and electrons. However, once ionised, electrons are given away or shared.

    Lets take your example of  V^{3+} . V by itself has an atomic number of 23 on the periodic table. That means it has 23 protons and 23 electrons. However, once ionised, V gives away 3 electrons and becomes  V^{3+} It now has a charge of 3 and has 23 protons and 3 electrons.

    Now for the second number, the bigger number called the mass number. Because electrons have much smaller masses than protons and neutrons, their mass is negligeble when calculating the mass of individual atoms. The mass number is defined as:

    Mass number = # of protons + # of neutrons.
    Since # of protons = atomic number, another way of saying this is:
    Mass number = Atomic Number + # of Neutrons. It is thus very straightforward to find the number of neutrons.

    The mass number is in decimals because it is an average masses of all isotopes weighted by abundance. Because we are most likely dealing with the most abundant isotope, just round the mass number to the nearest integer and proceed with your calculation.
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