Add the following fractions together. Leave the answer as an improper fraction. 1/3 + 5/4
To add fractions together, we need to first make sure that the denominators of the fractions are the same. In this problem, the denominators are not the same so we cannot immediately add them together. To get the denominators the same, we need to find the least common multiple. The multiples of 3 include 3, 6, 9, 12, 15, etc. The multiples of 4 include 4, 8, 12, 16, etc. As we can see, the lowest shared multiple of these two numbers is 12. We can use 12 as our common denominator. To convert 1/3 to a denominator of 12, I like to set it up as so: 1/3=?/12. From this, we can see that we multiplied 3 by 4 to get a denominator of 12. We need to multiply the numerator by 4 as well so that can get the correct converted fraction. 1 x 4 = 4. Therefore, the new fraction is 4/12. We can follow the same steps to convert the 5/4 fraction. Like before, we can set it up as: 5/4=?/12. Now we can see that we multiplied the denominator of 4 by 3 to get the new denominator of 12. We need to multiply the numerator of 5 by 3 to get the new numerator of 15. Now the new fraction is 15/12. The new equation is now: 4/12 + 15/12 With the same denominator, we can now add the numerators, but keep the denominator the same. 4 + 15 =19. Therefore, the product is now 19/12. Now, this new equation is an improper fraction. We could convert it, but the question specifically asks us to leave it as an improper fraction so our final answer is 19/12.
Phosphorus burns in O2 to form a combustion product that is 43.64% phosphorus and 56.36% oxygen. Determine the empirical formula of this reaction.
It is helpful to first start out these problems by writing a balanced chemical equation. Since phosphorus burns in O2, the equation should be P + O2 --> PO2. This equation is already balanced and now we can move on. The next step is to assume that we have 100 grams of the product. This way, the 43.64% phosphorus translates to 43.64 grams of phosphorus while 56.36% of oxygen translates to 56.36 grams of oxygen. We need phosphorus and oxygen in grams so that we can convert them to moles. To find out how many moles of phosphorus there is, we need to divide the amount of phosphorus in grams by its molar mass (Molar mass can be found in the periodic table). Therefore, we will divide 43.64 grams of phosphorus by its molar mass, 30.974 grams. We end up with 1.41 moles of phosphorus. We find the moles of oxygen the same way we found it for phosphorus. We divide 56.36 grams of oxygen by its molar mass, 15.999 grams. We end up with 3.52 moles of oxygen. Now that we have the mole amounts for both species, we need to divide the larger amount of moles by the smallest amount of moles. In this instance, we will divide 3.52 moles of oxygen by 1.41 moles of phosphorus. After this is complete, phosphorus has a subscript of 1 and oxygen has a subscript of 2.5. However, an empirical formula requires that all subscripts are whole numbers. To get oxygen's subscript to a whole number, we have to multiply it by another number. We can multiply oxygen's subscript of 2.5 by 2 to get it to a subscript of 5. However, when we multiply oxygen's subscript, we have to multiply phosphorus's subscript by the same amount which means 1 x 2= 2. Therefore, the empirical formula for the combustion product is P2O5.
It is important to understand the structure and function of the simplest life forms. Understanding the cell membrane is key to understanding basic biology. What factors can affect the permeability of the cell membrane?
To first understand the cell membrane, one must first understand that it is comprised of phospholipid bilayers that form spontaneously. Cell membranes are semi-permeable which means that they allow certain items to pass through, but not others. Factors that can affect the permeability of a cell's membrane include: 1 The length of the fatty acid tails that make up the phospholipid bilayers. The longer the tail, the more difficult it is for items to pass through the membrane. 2. The number of double bonds between the carbons in the phospholipid tail. If there are many double bonds within the tails, the tails will not be packed as closely together, leaving more space. This allows items to pass through more easily. 3. The number of cholesterol molecules within the membrane can also play a factor in a cell membrane's permeability. Since cholesterol is hydrophobic, an increase in cholesterol will result in a decrease in permeability. 4. Temperature: An increase in temperature results in an increase in permeability. Membrane fluidity will decrease with decreased temperature because the molecules in the bilayer will move more slowly. It is easier to pass through a membrane when the molecules are moving quickly.