1) Rate constant is a measure of the rate of the reaction. Larger the value of k, faster is the reaction and vice versa.
2) Different reactions have different values of k.
3) At a fixed temperature, the value of k is constant and is characteristic of the reaction. However it changes with temperature.
4) For a particular reaction, the reaction constant is independent of concentration.
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A constant is usually reffered as a 'k'.
'k' is derived by the ratio of two standard value. The other characteristics given above are absolutely correct, but I thought that it's important to give a idea about 'k'.
'k' also depends on the SI units used when the formula was derived.